Solve 23x^2=8

$$23 { x }^{ 2 } =8$$

Solve for x

$$x=\frac{2\sqrt{46}}{23}\approx 0.589767825$$

$$x=-\frac{2\sqrt{46}}{23}\approx -0.589767825$$

Steps by Finding Square Root

Divide both sides by 23.

$$x^{2}=\frac{8}{23}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{46}}{23} x=-\frac{2\sqrt{46}}{23}$$

Steps Using the Quadratic Formula

Divide both sides by 23.

$$x^{2}=\frac{8}{23}$$

Subtract \frac{8}{23} from both sides.

$$x^{2}-\frac{8}{23}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{8}{23} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{8}{23}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{8}{23}\right)}}{2}$$

Multiply -4 times -\frac{8}{23}.

$$x=\frac{0±\sqrt{\frac{32}{23}}}{2}$$

Take the square root of \frac{32}{23}.

$$x=\frac{0±\frac{4\sqrt{46}}{23}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{46}}{23}}{2} when ± is plus.

$$x=\frac{2\sqrt{46}}{23}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{46}}{23}}{2} when ± is minus.

$$x=-\frac{2\sqrt{46}}{23}$$

The equation is now solved.

$$x=\frac{2\sqrt{46}}{23} x=-\frac{2\sqrt{46}}{23}$$