What Is The Intermediate Step In The Form $(x+a)^2=b$ As A Result Of Completing The Square For The Following Equation?$5x^2 + 380 = 90x - 10$

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What is the Intermediate Step in the Form $(x+a)^2=b$ as a Result of Completing the Square for the Following Equation? 5x2+380=90x−105x^2 + 380 = 90x - 10

Completing the square is a powerful technique used in algebra to solve quadratic equations. It involves rewriting a quadratic equation in a form that allows us to easily identify the solutions. In this article, we will explore the intermediate step in the form $(x+a)^2=b$ as a result of completing the square for the equation 5x2+380=90x−105x^2 + 380 = 90x - 10.

The given equation is 5x2+380=90x−105x^2 + 380 = 90x - 10. To complete the square, we need to rewrite this equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0. We can do this by subtracting 380380 from both sides of the equation and adding 1010 to both sides.

5x2+380−380=90x−10−3805x^2 + 380 - 380 = 90x - 10 - 380

This simplifies to:

5x2=90x−3905x^2 = 90x - 390

To complete the square, we need to move the constant term to the right-hand side of the equation. We can do this by subtracting 390390 from both sides of the equation.

5x2−90x=−3905x^2 - 90x = -390

Next, we need to divide both sides of the equation by 55 to get:

x2−18x=−78x^2 - 18x = -78

Now, we need to find the intermediate step in the form $(x+a)^2=b$. To do this, we need to add and subtract (18/2)2=81(18/2)^2 = 81 to the left-hand side of the equation.

x2−18x+81−81=−78x^2 - 18x + 81 - 81 = -78

This simplifies to:

(x−9)2−81=−78(x - 9)^2 - 81 = -78

Now, we can add 8181 to both sides of the equation to get:

(x−9)2=−78+81(x - 9)^2 = -78 + 81

This simplifies to:

(x−9)2=3(x - 9)^2 = 3

In this article, we explored the intermediate step in the form $(x+a)^2=b$ as a result of completing the square for the equation 5x2+380=90x−105x^2 + 380 = 90x - 10. We started by rewriting the equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0. Then, we completed the square by moving the constant term to the right-hand side of the equation and adding and subtracting (18/2)2=81(18/2)^2 = 81 to the left-hand side of the equation. Finally, we simplified the equation to get the final result in the form $(x+a)^2=b$.
Frequently Asked Questions (FAQs) on Completing the Square

Completing the square is a powerful technique used in algebra to solve quadratic equations. In our previous article, we explored the intermediate step in the form $(x+a)^2=b$ as a result of completing the square for the equation 5x2+380=90x−105x^2 + 380 = 90x - 10. In this article, we will answer some frequently asked questions (FAQs) on completing the square.

A: Completing the square is a technique used to rewrite a quadratic equation in the form $(x+a)^2=b$. This allows us to easily identify the solutions to the equation.

A: We need to complete the square because it allows us to easily identify the solutions to a quadratic equation. By rewriting the equation in the form $(x+a)^2=b$, we can use the square root property to find the solutions.

A: To complete the square, you need to follow these steps:

  1. Rewrite the equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0.
  2. Move the constant term to the right-hand side of the equation.
  3. Add and subtract (b/2)2(b/2)^2 to the left-hand side of the equation.
  4. Simplify the equation to get the final result in the form $(x+a)^2=b$.

A: The intermediate step in completing the square is the step where you add and subtract (b/2)2(b/2)^2 to the left-hand side of the equation. This step is crucial in rewriting the equation in the form $(x+a)^2=b$.

A: You should complete the square when you are given a quadratic equation and you need to find the solutions. Completing the square is a powerful technique that can be used to solve quadratic equations that cannot be factored.

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 (b/2)2(b/2)^2 to the left-hand side of the equation.
  • Not simplifying the equation to get the final result in the form $(x+a)^2=b$.

A: Yes, you can use completing the square to solve quadratic equations with complex coefficients. However, you need to be careful when working with complex numbers and make sure to follow the correct steps.

In this article, we answered some frequently asked questions (FAQs) on completing the square. We covered topics such as what completing the square is, why we need to complete the square, how to complete the square, and some common mistakes to avoid. We hope that this article has been helpful in understanding the concept of completing the square.