Solve 4(x-8)^2-10=14

$$4 ( x - 8 ) ^ { 2 } - 10 = 14$$

Solve for x

$$x=\sqrt{6}+8\approx 10.449489743$$

$$x=8-\sqrt{6}\approx 5.550510257$$

Steps by Finding Square Root

Add 10 to both sides of the equation.

$$4\left(x-8\right)^{2}-10+10=14+10$$

Subtracting 10 from itself leaves 0.

$$4\left(x-8\right)^{2}=14+10$$

Add 14 to 10.

$$4\left(x-8\right)^{2}=24$$

Divide both sides by 4.

$$\frac{4\left(x-8\right)^{2}}{4}=\frac{24}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\left(x-8\right)^{2}=\frac{24}{4}$$

Divide 24 by 4.

$$\left(x-8\right)^{2}=6$$

Take the square root of both sides of the equation.

$$x-8=\sqrt{6} x-8=-\sqrt{6}$$

Add 8 to both sides of the equation.

$$x-8-\left(-8\right)=\sqrt{6}-\left(-8\right) x-8-\left(-8\right)=-\sqrt{6}-\left(-8\right)$$

Subtracting -8 from itself leaves 0.

$$x=\sqrt{6}-\left(-8\right) x=-\sqrt{6}-\left(-8\right)$$

Subtract -8 from \sqrt{6}.

$$x=\sqrt{6}+8$$

Subtract -8 from -\sqrt{6}.

$$x=8-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6}+8 x=8-\sqrt{6}$$