Determine Whether The Statement Is True Or False:58 Is A Solution Of X + 6 = X − 54 − 3 \sqrt{\sqrt{x} + 6} = \sqrt{x} - 54 - 3 X ​ + 6 ​ = X ​ − 54 − 3 .Choose The Correct Answer Below:A. The Statement Is True Because After Solving The Equation, The Solution Is X = 58 X = 58 X = 58 .B.

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Introduction

In this article, we will determine whether the statement "58 is a solution of $\sqrt{\sqrt{x} + 6} = \sqrt{x} - 54 - 3$" is true or false. To do this, we will first analyze the given equation and then solve for $x$ to see if $x = 58$ is a valid solution.

Step 1: Simplify the equation

The given equation is $\sqrt{\sqrt{x} + 6} = \sqrt{x} - 54 - 3$. To simplify this equation, we can start by isolating the square root terms.

$\sqrt{\sqrt{x} + 6} = \sqrt{x} - 54 - 3$

Step 2: Square both sides of the equation

To eliminate the square roots, we can square both sides of the equation.

$(\sqrt{\sqrt{x} + 6})^2 = (\sqrt{x} - 54 - 3)^2$

Step 3: Expand the squared terms

Expanding the squared terms, we get:

$\sqrt{x} + 6 = x - 2\sqrt{x}(54 + 3) + (54 + 3)^2$

Step 4: Simplify the equation

Simplifying the equation, we get:

$\sqrt{x} + 6 = x - 2\sqrt{x}(57) + 57^2$

Step 5: Rearrange the terms

Rearranging the terms, we get:

$\sqrt{x} + 6 = x - 114\sqrt{x} + 3249$

Step 6: Move all terms to one side of the equation

Moving all terms to one side of the equation, we get:

$114\sqrt{x} - \sqrt{x} = x - 3249 - 6$

Step 7: Factor out the square root term

Factoring out the square root term, we get:

$113\sqrt{x} = x - 3255$

Step 8: Square both sides of the equation again

To eliminate the square root term, we can square both sides of the equation again.

$(113\sqrt{x})^2 = (x - 3255)^2$

Step 9: Expand the squared terms

Expanding the squared terms, we get:

$12769x = x^2 - 2x(3255) + 3255^2$

Step 10: Simplify the equation

Simplifying the equation, we get:

$12769x = x^2 - 6510x + 10576225$

Step 11: Rearrange the terms

Rearranging the terms, we get:

$0 = x^2 - 7799x + 10576225$

Step 12: Solve for x

To solve for $x$, we can use the quadratic formula.

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Step 13: Plug in the values

Plugging in the values, we get:

$x = \frac{-(-7799) \pm \sqrt{(-7799)^2 - 4(1)(10576225)}}{2(1)}$

Step 14: Simplify the equation

Simplifying the equation, we get:

$x = \frac{7799 \pm \sqrt{60960001 - 42304900}}{2}$

Step 15: Simplify the equation further

Simplifying the equation further, we get:

$x = \frac{7799 \pm \sqrt{18655101}}{2}$

Step 16: Simplify the equation even further

Simplifying the equation even further, we get:

$x = \frac{7799 \pm 4327}{2}$

Step 17: Solve for x

Solving for $x$, we get two possible values:

$x = \frac{7799 + 4327}{2}$

$x = \frac{7799 - 4327}{2}$

Step 18: Simplify the equation

Simplifying the equation, we get:

$x = 6063$

$x = 1736$

Step 19: Check if x = 58 is a solution

Since $x = 58$ is not one of the solutions, we can conclude that the statement "58 is a solution of $\sqrt{\sqrt{x} + 6} = \sqrt{x} - 54 - 3$" is false.

The final answer is: B

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Introduction

In our previous article, we determined that the statement "58 is a solution of $\sqrt{\sqrt{x} + 6} = \sqrt{x} - 54 - 3$" is false. However, we received many questions from readers who wanted to know more about the solution process and how to determine whether a statement is true or false. In this article, we will answer some of the most frequently asked questions.

Q: What is the correct solution to the equation?

A: The correct solution to the equation is $x = 6063$ or $x = 1736$. These are the two possible values of $x$ that satisfy the equation.

Q: Why is $x = 58$ not a solution?

A: $x = 58$ is not a solution because it does not satisfy the equation. When we plug in $x = 58$ into the equation, we get a value that is not equal to the right-hand side of the equation.

Q: Can you explain the steps to solve the equation?

A: Yes, we can explain the steps to solve the equation. The steps are as follows:

1. Simplify the equation by isolating the square root terms.
2. Square both sides of the equation to eliminate the square roots.
3. Expand the squared terms and simplify the equation.
4. Rearrange the terms and move all terms to one side of the equation.
5. Factor out the square root term and square both sides of the equation again.
6. Expand the squared terms and simplify the equation.
7. Rearrange the terms and solve for $x$ using the quadratic formula.

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that is used to solve quadratic equations. The formula is as follows:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Q: Can you explain the quadratic formula in more detail?

A: Yes, we can explain the quadratic formula in more detail. The quadratic formula is used to solve quadratic equations of the form $ax^2 + bx + c = 0$. The formula is based on the fact that the solutions to a quadratic equation can be expressed in terms of the coefficients of the equation.

Q: What are the coefficients of the quadratic equation?

A: The coefficients of the quadratic equation are $a$, $b$, and $c$. In the equation $x^2 - 7799x + 10576225 = 0$, the coefficients are $a = 1$, $b = -7799$, and $c = 10576225$.

Q: How do you use the quadratic formula to solve the equation?

A: To use the quadratic formula to solve the equation, you need to plug in the values of $a$, $b$, and $c$ into the formula. In this case, the values are $a = 1$, $b = -7799$, and $c = 10576225$. Plugging these values into the formula, we get:

$x = \frac{-(-7799) \pm \sqrt{(-7799)^2 - 4(1)(10576225)}}{2(1)}$

Q: Can you simplify the equation further?

A: Yes, we can simplify the equation further. Simplifying the equation, we get:

$x = \frac{7799 \pm \sqrt{60960001 - 42304900}}{2}$

Q: Can you simplify the equation even further?

A: Yes, we can simplify the equation even further. Simplifying the equation, we get:

$x = \frac{7799 \pm \sqrt{18655101}}{2}$

Q: Can you simplify the equation even further?

A: Yes, we can simplify the equation even further. Simplifying the equation, we get:

$x = \frac{7799 \pm 4327}{2}$

Q: What are the two possible values of $x$?

A: The two possible values of $x$ are $x = 6063$ and $x = 1736$.

Q: Why is $x = 58$ not a solution?

A: $x = 58$ is not a solution because it does not satisfy the equation. When we plug in $x = 58$ into the equation, we get a value that is not equal to the right-hand side of the equation.

Q: Can you explain the solution process in more detail?

A: Yes, we can explain the solution process in more detail. The solution process involves simplifying the equation, squaring both sides of the equation, expanding the squared terms, and rearranging the terms. The final step is to solve for $x$ using the quadratic formula.

Q: What is the final answer?

A: The final answer is that the statement "58 is a solution of $\sqrt{\sqrt{x} + 6} = \sqrt{x} - 54 - 3$" is false. The correct solutions to the equation are $x = 6063$ and $x = 1736$.