Solve 5(x+15)^2-7=0

$$5 ( x + 15 ) ^ { 2 } - 7 = 0$$

Solve for x

$$x=\frac{\sqrt{35}}{5}-15\approx -13.816784043$$

$$x=-\frac{\sqrt{35}}{5}-15\approx -16.183215957$$

Steps by Finding Square Root

Add 7 to both sides of the equation.

$$5\left(x+15\right)^{2}-7+7=7$$

Subtracting 7 from itself leaves 0.

$$5\left(x+15\right)^{2}=7$$

Divide both sides by 5.

$$\frac{5\left(x+15\right)^{2}}{5}=\frac{7}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\left(x+15\right)^{2}=\frac{7}{5}$$

Take the square root of both sides of the equation.

$$x+15=\frac{\sqrt{35}}{5} x+15=-\frac{\sqrt{35}}{5}$$

Subtract 15 from both sides of the equation.

$$x+15-15=\frac{\sqrt{35}}{5}-15 x+15-15=-\frac{\sqrt{35}}{5}-15$$

Subtracting 15 from itself leaves 0.

$$x=\frac{\sqrt{35}}{5}-15 x=-\frac{\sqrt{35}}{5}-15$$