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$(x-10)^2 = 121$

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Describe the graph of a linear equation

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Q.

(x-10)^2 = 121

Understand the equation: Understand the equation. $\newline$ We have the equation $(x-10)^2 = 121$ , which is a quadratic equation in the form of a perfect square equal to a positive number.
Take square root: Take the square root of both sides. $\newline$ To solve for $x$ , we need to take the square root of both sides of the equation. This will give us two possible solutions because the square root of a number can be both positive and negative. $\newline$ $\sqrt{(x-10)^2} = \pm\sqrt{121}$
Simplify square root: Simplify the square root. $\newline$ The square root of $(x-10)^2$ is $x-10$ , and the square root of $121$ is $11$ . $\newline$ $x - 10 = \pm11$
Solve for x (positive): Solve for x when the square root is positive. $\newline$ First, we will consider the positive square root. $\newline$ $x - 10 = 11$ $\newline$ Add $10$ to both sides to isolate x. $\newline$ $x = 11 + 10$ $\newline$ $x = 21$
Solve for x (negative): Solve for x when the square root is negative. $\newline$ Now, we will consider the negative square root. $\newline$ $x - 10 = -11$ $\newline$ Add $10$ to both sides to isolate x. $\newline$ $x = -11 + 10$ $\newline$ $x = -1$

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