Solve (x-4)^2-31=30

$$( x - 4 ) ^ { 2 } - 31 = 30$$

Solve for x

$$x=\sqrt{61}+4\approx 11.810249676$$

$$x=4-\sqrt{61}\approx -3.810249676$$

Steps by Finding Square Root

Add 31 to both sides of the equation.

$$\left(x-4\right)^{2}-31+31=30+31$$

Subtracting 31 from itself leaves 0.

$$\left(x-4\right)^{2}=30+31$$

Add 30 to 31.

$$\left(x-4\right)^{2}=61$$

Take the square root of both sides of the equation.

$$x-4=\sqrt{61} x-4=-\sqrt{61}$$

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=\sqrt{61}-\left(-4\right) x-4-\left(-4\right)=-\sqrt{61}-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=\sqrt{61}-\left(-4\right) x=-\sqrt{61}-\left(-4\right)$$

Subtract -4 from \sqrt{61}.

$$x=\sqrt{61}+4$$

Subtract -4 from -\sqrt{61}.

$$x=4-\sqrt{61}$$

The equation is now solved.

$$x=\sqrt{61}+4 x=4-\sqrt{61}$$