Solve Using the Square Root Property (x-3)^2=196

${(x - 3)}^{2} = 196$

Step 1

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

$x - 3 = \pm \sqrt{196}$

Step 2

Simplify $\pm \sqrt{196}$ .

Rewrite $196$ as $14^{2}$ .

$x - 3 = \pm \sqrt{14^{2}}$

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

$x - 3 = \pm 14$

Step 3

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.

$x - 3 = 14$

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

Add $3$ to both sides of the equation.

$x = 14 + 3$

Add $14$ and $3$ .

$x = 17$

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

$x - 3 = - 14$

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

Add $3$ to both sides of the equation.

$x = - 14 + 3$

Add $- 14$ and $3$ .

$x = - 11$

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

$x = 17, - 11$