Solve Using the Square Root Property (x-14)^2+13=12

${(x - 14)}^{2} + 13 = 12$

Subtract $13$ from both sides of the equation.

${(x - 14)}^{2} = 12 - 13$

Subtract $13$ from $12$ .

${(x - 14)}^{2} = - 1$

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

$x - 14 = \pm \sqrt{- 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x - 14 = \pm i$

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.

$x - 14 = i$

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

Add $14$ to both sides of the equation.

$x = i + 14$

Reorder $i$ and $14$ .

$x = 14 + i$

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

$x - 14 = - i$

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

Add $14$ to both sides of the equation.

$x = - i + 14$

Reorder $- i$ and $14$ .

$x = 14 - i$

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

$x = 14 + i, 14 - i$