Solve (x-4)^2=7

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

Solve for x

$$x=\sqrt{7}+4\approx 6.645751311$$

$$x=4-\sqrt{7}\approx 1.354248689$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-4=\sqrt{7} x-4=-\sqrt{7}$$

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=\sqrt{7}-\left(-4\right) x-4-\left(-4\right)=-\sqrt{7}-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=\sqrt{7}-\left(-4\right) x=-\sqrt{7}-\left(-4\right)$$

Subtract -4 from \sqrt{7}.

$$x=\sqrt{7}+4$$

Subtract -4 from -\sqrt{7}.

$$x=4-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7}+4 x=4-\sqrt{7}$$