Solve 10(x-7)^2=440

$$10 ( x - 7 ) ^ { 2 } = 440$$

Solve for x

$$x=2\sqrt{11}+7\approx 13.633249581$$

$$x=7-2\sqrt{11}\approx 0.366750419$$

Steps by Finding Square Root

Divide both sides by 10.

$$\frac{10\left(x-7\right)^{2}}{10}=\frac{440}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$\left(x-7\right)^{2}=\frac{440}{10}$$

Divide 440 by 10.

$$\left(x-7\right)^{2}=44$$

Take the square root of both sides of the equation.

$$x-7=2\sqrt{11} x-7=-2\sqrt{11}$$

Add 7 to both sides of the equation.

$$x-7-\left(-7\right)=2\sqrt{11}-\left(-7\right) x-7-\left(-7\right)=-2\sqrt{11}-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$x=2\sqrt{11}-\left(-7\right) x=-2\sqrt{11}-\left(-7\right)$$

Subtract -7 from 2\sqrt{11}.

$$x=2\sqrt{11}+7$$

Subtract -7 from -2\sqrt{11}.

$$x=7-2\sqrt{11}$$

The equation is now solved.

$$x=2\sqrt{11}+7 x=7-2\sqrt{11}$$