Solve 9-8-8x^2=0

$$9 - 8 - 8 x ^ { 2 } = 0$$

Solve for x

$$x=\frac{\sqrt{2}}{4}\approx 0.353553391$$

$$x=-\frac{\sqrt{2}}{4}\approx -0.353553391$$

Steps by Finding Square Root

Subtract 8 from 9 to get 1.

$$1-8x^{2}=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-8x^{2}=-1$$

Divide both sides by -8.

$$x^{2}=\frac{-1}{-8}$$

Fraction \frac{-1}{-8} can be simplified to \frac{1}{8} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{1}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{2}}{4} x=-\frac{\sqrt{2}}{4}$$

Steps Using the Quadratic Formula

Subtract 8 from 9 to get 1.

$$1-8x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-8x^{2}+1=0$$

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

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

Square 0.

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

Multiply -4 times -8.

$$x=\frac{0±\sqrt{32}}{2\left(-8\right)}$$

Take the square root of 32.

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

Multiply 2 times -8.

$$x=\frac{0±4\sqrt{2}}{-16}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{-16} when ± is plus.

$$x=-\frac{\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{-16} when ± is minus.

$$x=\frac{\sqrt{2}}{4}$$

The equation is now solved.

$$x=-\frac{\sqrt{2}}{4} x=\frac{\sqrt{2}}{4}$$