Solve for x 7+(x-4)^2=11

$7 + {(x - 4)}^{2} = 11$

Subtract $7$ from both sides of the equation.

${(x - 4)}^{2} = 11 - 7$

Subtract $7$ from $11$ .

${(x - 4)}^{2} = 4$

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

$x - 4 = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x - 4 = \pm \sqrt{2^{2}}$

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

$x - 4 = \pm 2$

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.

$x - 4 = 2$

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

Add $4$ to both sides of the equation.

$x = 2 + 4$

Add $2$ and $4$ .

$x = 6$

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

$x - 4 = - 2$

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

Add $4$ to both sides of the equation.

$x = - 2 + 4$

Add $- 2$ and $4$ .

$x = 2$

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

$x = 6, 2$