Susu Is Solving The Quadratic Equation 4 X 2 − 8 X − 13 = 0 4x^2 - 8x - 13 = 0 4 X 2 − 8 X − 13 = 0 By Completing The Square. Her First Four Steps Are Shown In The Table.Susu's Work$[ \begin{tabular}{|l|l|} \hline & 4 X 2 − 8 X − 13 = 0 4x^2 - 8x - 13 = 0 4 X 2 − 8 X − 13 = 0 \ \hline Step 1 & 4 X 2 − 8 X = 13 4x^2 - 8x = 13 4 X 2 − 8 X = 13

Introduction

Solving quadratic equations is a fundamental concept in mathematics, and one of the methods used to solve them is by completing the square. This method involves manipulating the quadratic equation to express it in a perfect square trinomial form, which can then be easily solved. In this article, we will explore how Susu is solving the quadratic equation $4x^2 - 8x - 13 = 0$ by completing the square.

Understanding the Method of Completing the Square

The method of completing the square is a technique used to solve quadratic equations of the form $ax^2 + bx + c = 0$. The basic idea behind this method is to manipulate the quadratic equation to express it in the form $(x + p)^2 = q$, where $p$ and $q$ are constants. This can be done by adding and subtracting a constant term to the quadratic equation, which allows us to express it as a perfect square trinomial.

Susu's Work

Let's take a look at Susu's work in solving the quadratic equation $4x^2 - 8x - 13 = 0$ by completing the square.

Step 1: Move the Constant Term to the Right-Hand Side

Susu starts by moving the constant term to the right-hand side of the equation.

$4x^2 - 8x = 13$

Step 2: Divide Both Sides by the Coefficient of the $x^2$ Term

Next, Susu divides both sides of the equation by the coefficient of the $x^2$ term, which is 4.

$x^2 - 2x = \frac{13}{4}$

Step 3: Add and Subtract the Square of Half the Coefficient of the $x$ Term

Now, Susu adds and subtracts the square of half the coefficient of the $x$ term, which is $(-2)^2 = 4$, to the left-hand side of the equation.

$x^2 - 2x + 4 - 4 = \frac{13}{4}$

Step 4: Express the Left-Hand Side as a Perfect Square Trinomial

Finally, Susu expresses the left-hand side of the equation as a perfect square trinomial.

$(x - 1)^2 - 4 = \frac{13}{4}$

Step 5: Add 4 to Both Sides of the Equation

Next, Susu adds 4 to both sides of the equation to isolate the perfect square trinomial.

$(x - 1)^2 = \frac{13}{4} + 4$

Step 6: Simplify the Right-Hand Side of the Equation

Susu simplifies the right-hand side of the equation by combining the fractions.

$(x - 1)^2 = \frac{13 + 16}{4}$

Step 7: Take the Square Root of Both Sides of the Equation

Now, Susu takes the square root of both sides of the equation to solve for $x$.

$x - 1 = \pm \sqrt{\frac{29}{4}}$

Step 8: Add 1 to Both Sides of the Equation

Finally, Susu adds 1 to both sides of the equation to solve for $x$.

$x = 1 \pm \sqrt{\frac{29}{4}}$

Conclusion

In this article, we have seen how Susu is solving the quadratic equation $4x^2 - 8x - 13 = 0$ by completing the square. By following the steps outlined above, Susu is able to express the quadratic equation in a perfect square trinomial form, which can then be easily solved. This method is a powerful tool for solving quadratic equations and is an important concept in mathematics.

Tips and Tricks

• When completing the square, make sure to add and subtract the same constant term to both sides of the equation.
• When taking the square root of both sides of the equation, make sure to consider both the positive and negative square roots.
• When simplifying the right-hand side of the equation, make sure to combine any like terms.

Practice Problems

• Solve the quadratic equation $x^2 + 6x + 8 = 0$ by completing the square.
• Solve the quadratic equation $2x^2 - 4x - 5 = 0$ by completing the square.
• Solve the quadratic equation $x^2 - 2x - 6 = 0$ by completing the square.

References

• [1] "Completing the Square" by Math Open Reference
• [2] "Solving Quadratic Equations by Completing the Square" by Khan Academy
• [3] "Completing the Square" by Purplemath

Glossary

• Completing the Square: A method used to solve quadratic equations by expressing them in a perfect square trinomial form.
• Perfect Square Trinomial: A trinomial that can be expressed as the square of a binomial.
• Binomial: An expression consisting of two terms separated by a plus or minus sign.
• Coefficient: A number that is multiplied by a variable in an algebraic expression.
  Solving Quadratic Equations by Completing the Square: A Q&A Guide ================================================================

Introduction

Solving quadratic equations is a fundamental concept in mathematics, and one of the methods used to solve them is by completing the square. In our previous article, we explored how Susu is solving the quadratic equation $4x^2 - 8x - 13 = 0$ by completing the square. In this article, we will answer some of the most frequently asked questions about solving quadratic equations by completing the square.

Q&A

Q: What is completing the square?

A: Completing the square is a method used to solve quadratic equations by expressing them in a perfect square trinomial form. This involves adding and subtracting a constant term to the quadratic equation, which allows us to express it as a perfect square trinomial.

Q: How do I know when to use completing the square?

A: You should use completing the square when the quadratic equation is in the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. This method is particularly useful when the quadratic equation has a negative discriminant.

Q: What is the first step in completing the square?

A: The first step in completing the square is to move the constant term to the right-hand side of the equation. This will give you a quadratic equation in the form $ax^2 + bx = c$.

Q: How do I add and subtract the constant term to complete the square?

A: To add and subtract the constant term, you need to add and subtract the square of half the coefficient of the $x$ term. This will give you a perfect square trinomial on the left-hand side of the equation.

Q: What is the next step after completing the square?

A: After completing the square, you need to take the square root of both sides of the equation to solve for $x$. This will give you two possible solutions for $x$.

Q: Can I use completing the square to solve quadratic equations with complex coefficients?

A: Yes, you can use completing the square to solve quadratic equations with complex coefficients. However, you need to be careful when taking the square root of complex numbers.

Q: What are some common mistakes to avoid when completing the square?

A: Some common mistakes to avoid when completing the square include:

• Not moving the constant term to the right-hand side of the equation
• Not adding and subtracting the correct constant term
• Not taking the square root of both sides of the equation
• Not considering both the positive and negative square roots

Tips and Tricks

• Make sure to add and subtract the same constant term to both sides of the equation.
• Make sure to take the square root of both sides of the equation.
• Make sure to consider both the positive and negative square roots.
• Make sure to simplify the right-hand side of the equation.

Practice Problems

• Solve the quadratic equation $x^2 + 6x + 8 = 0$ by completing the square.
• Solve the quadratic equation $2x^2 - 4x - 5 = 0$ by completing the square.
• Solve the quadratic equation $x^2 - 2x - 6 = 0$ by completing the square.

References

• [1] "Completing the Square" by Math Open Reference
• [2] "Solving Quadratic Equations by Completing the Square" by Khan Academy
• [3] "Completing the Square" by Purplemath

Glossary

• Completing the Square: A method used to solve quadratic equations by expressing them in a perfect square trinomial form.
• Perfect Square Trinomial: A trinomial that can be expressed as the square of a binomial.
• Binomial: An expression consisting of two terms separated by a plus or minus sign.
• Coefficient: A number that is multiplied by a variable in an algebraic expression.

Conclusion

In this article, we have answered some of the most frequently asked questions about solving quadratic equations by completing the square. We hope that this article has been helpful in clarifying the concept of completing the square and providing you with a better understanding of how to solve quadratic equations using this method.