Solve 2(x-4)^2=26

$$2 ( x - 4 ) ^ { 2 } = 26$$

Solve for x

$$x=\sqrt{13}+4\approx 7.605551275$$

$$x=4-\sqrt{13}\approx 0.394448725$$

Steps by Finding Square Root

Divide both sides by 2.

$$\frac{2\left(x-4\right)^{2}}{2}=\frac{26}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\left(x-4\right)^{2}=\frac{26}{2}$$

Divide 26 by 2.

$$\left(x-4\right)^{2}=13$$

Take the square root of both sides of the equation.

$$x-4=\sqrt{13} x-4=-\sqrt{13}$$

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=\sqrt{13}-\left(-4\right) x-4-\left(-4\right)=-\sqrt{13}-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=\sqrt{13}-\left(-4\right) x=-\sqrt{13}-\left(-4\right)$$

Subtract -4 from \sqrt{13}.

$$x=\sqrt{13}+4$$

Subtract -4 from -\sqrt{13}.

$$x=4-\sqrt{13}$$

The equation is now solved.

$$x=\sqrt{13}+4 x=4-\sqrt{13}$$