Understand the equation: Understand the equation. 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. 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. √((x-10)^2) = ±√121Simplify square root: Simplify the square root. The square root of (x-10)^2 is x-10, and the square root of 121 is 11. x - 10 = ±11Solve for x (positive): Solve for x when the square root is positive. First, we will consider the positive square root. x - 10 = 11 Add 10 to both sides to isolate x. x = 11 + 10 x = 21Solve for x (negative): Solve for x when the square root is negative. Now, we will consider the negative square root. x - 10 = -11 Add 10 to both sides to isolate x. x = -11 + 10 x = -1

Grade 8

Describe the graph of a linear equation

Full solution

(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. $\newline$ $x = -11 + 10$ $\newline$ $x = -1$