Solve 2(x-10)^2-48=0

$$2 ( x - 10 ) ^ { 2 } - 48 = 0$$

Solve for x

$$x=2\sqrt{6}+10\approx 14.898979486$$

$$x=10-2\sqrt{6}\approx 5.101020514$$

Steps by Finding Square Root

Add 48 to both sides of the equation.

$$2\left(x-10\right)^{2}-48+48=48$$

Subtracting 48 from itself leaves 0.

$$2\left(x-10\right)^{2}=48$$

Divide both sides by 2.

$$\frac{2\left(x-10\right)^{2}}{2}=\frac{48}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\left(x-10\right)^{2}=\frac{48}{2}$$

Divide 48 by 2.

$$\left(x-10\right)^{2}=24$$

Take the square root of both sides of the equation.

$$x-10=2\sqrt{6} x-10=-2\sqrt{6}$$

Add 10 to both sides of the equation.

$$x-10-\left(-10\right)=2\sqrt{6}-\left(-10\right) x-10-\left(-10\right)=-2\sqrt{6}-\left(-10\right)$$

Subtracting -10 from itself leaves 0.

$$x=2\sqrt{6}-\left(-10\right) x=-2\sqrt{6}-\left(-10\right)$$

Subtract -10 from 2\sqrt{6}.

$$x=2\sqrt{6}+10$$

Subtract -10 from -2\sqrt{6}.

$$x=10-2\sqrt{6}$$

The equation is now solved.

$$x=2\sqrt{6}+10 x=10-2\sqrt{6}$$