Solve 2(z+19)^2-50=130

$$2 ( z + 19 ) ^ { 2 } - 50 = 130$$

Solve for z

$$z=3\sqrt{10}-19\approx -9.513167019$$

$$z=-3\sqrt{10}-19\approx -28.486832981$$

Steps by Finding Square Root

Add 50 to both sides of the equation.

$$2\left(z+19\right)^{2}-50+50=130+50$$

Subtracting 50 from itself leaves 0.

$$2\left(z+19\right)^{2}=130+50$$

Add 130 to 50.

$$2\left(z+19\right)^{2}=180$$

Divide both sides by 2.

$$\frac{2\left(z+19\right)^{2}}{2}=\frac{180}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\left(z+19\right)^{2}=\frac{180}{2}$$

Divide 180 by 2.

$$\left(z+19\right)^{2}=90$$

Take the square root of both sides of the equation.

$$z+19=3\sqrt{10} z+19=-3\sqrt{10}$$

Subtract 19 from both sides of the equation.

$$z+19-19=3\sqrt{10}-19 z+19-19=-3\sqrt{10}-19$$

Subtracting 19 from itself leaves 0.

$$z=3\sqrt{10}-19 z=-3\sqrt{10}-19$$