Find the Roots (Zeros) f(x)=(x-10)^2-49

$f (x) = {(x - 10)}^{2} - 49$

Step 1

Set ${(x - 10)}^{2} - 49$ equal to $0$ .

${(x - 10)}^{2} - 49 = 0$

Step 2

Solve for $x$ .

Add $49$ to both sides of the equation.

${(x - 10)}^{2} = 49$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x - 10 = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$x - 10 = \pm \sqrt{7^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x - 10 = \pm 7$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x - 10 = 7$

Move all terms not containing $x$ to the right side of the equation.

Add $10$ to both sides of the equation.

$x = 7 + 10$

Add $7$ and $10$ .

$x = 17$

Next, use the negative value of the $\pm$ to find the second solution.

$x - 10 = - 7$

Move all terms not containing $x$ to the right side of the equation.

Add $10$ to both sides of the equation.

$x = - 7 + 10$

Add $- 7$ and $10$ .

$x = 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 17, 3$

Step 3