Solve (5-x)^2=7

$$( 5 - x ) ^ { 2 } = 7$$

Solve for x

$$x=5-\sqrt{7}\approx 2.354248689$$

$$x=\sqrt{7}+5\approx 7.645751311$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$-x+5=\sqrt{7} -x+5=-\sqrt{7}$$

Subtract 5 from both sides of the equation.

$$-x+5-5=\sqrt{7}-5 -x+5-5=-\sqrt{7}-5$$

Subtracting 5 from itself leaves 0.

$$-x=\sqrt{7}-5 -x=-\sqrt{7}-5$$

Subtract 5 from \sqrt{7}.

$$-x=\sqrt{7}-5$$

Subtract 5 from -\sqrt{7}.

$$-x=-\sqrt{7}-5$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\sqrt{7}-5}{-1} \frac{-x}{-1}=\frac{-\sqrt{7}-5}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\sqrt{7}-5}{-1} x=\frac{-\sqrt{7}-5}{-1}$$

Divide \sqrt{7}-5 by -1.

$$x=5-\sqrt{7}$$

Divide -\sqrt{7}-5 by -1.

$$x=\sqrt{7}+5$$

The equation is now solved.

$$x=5-\sqrt{7} x=\sqrt{7}+5$$