Solve for x (x-2)^2+46=47

${(x - 2)}^{2} + 46 = 47$

Subtract $46$ from both sides of the equation.

${(x - 2)}^{2} = 47 - 46$

Subtract $46$ from $47$ .

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

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

$x - 2 = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x - 2 = \pm 1$

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.

$x - 2 = 1$

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

Add $2$ to both sides of the equation.

$x = 1 + 2$

Add $1$ and $2$ .

$x = 3$

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

$x - 2 = - 1$

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

Add $2$ to both sides of the equation.

$x = - 1 + 2$

Add $- 1$ and $2$ .

$x = 1$

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

$x = 3, 1$