Solve 3(x-8)^2-19=0

$$3 ( x - 8 ) ^ { 2 } - 19 = 0$$

Solve for x

$$x=\frac{\sqrt{57}}{3}+8\approx 10.516611478$$

$$x=-\frac{\sqrt{57}}{3}+8\approx 5.483388522$$

Steps by Finding Square Root

Add 19 to both sides of the equation.

$$3\left(x-8\right)^{2}-19+19=19$$

Subtracting 19 from itself leaves 0.

$$3\left(x-8\right)^{2}=19$$

Divide both sides by 3.

$$\frac{3\left(x-8\right)^{2}}{3}=\frac{19}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(x-8\right)^{2}=\frac{19}{3}$$

Take the square root of both sides of the equation.

$$x-8=\frac{\sqrt{57}}{3} x-8=-\frac{\sqrt{57}}{3}$$

Add 8 to both sides of the equation.

$$x-8-\left(-8\right)=\frac{\sqrt{57}}{3}-\left(-8\right) x-8-\left(-8\right)=-\frac{\sqrt{57}}{3}-\left(-8\right)$$

Subtracting -8 from itself leaves 0.

$$x=\frac{\sqrt{57}}{3}-\left(-8\right) x=-\frac{\sqrt{57}}{3}-\left(-8\right)$$

Subtract -8 from \frac{\sqrt{57}}{3}.

$$x=\frac{\sqrt{57}}{3}+8$$

Subtract -8 from -\frac{\sqrt{57}}{3}.

$$x=-\frac{\sqrt{57}}{3}+8$$

The equation is now solved.

$$x=\frac{\sqrt{57}}{3}+8 x=-\frac{\sqrt{57}}{3}+8$$