Solve 8x^2+1=2

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

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 1 from both sides.

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

Subtract 1 from 2 to get 1.

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

Divide both sides by 8.

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

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 2 from both sides.

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

Subtract 2 from 1 to get -1.

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

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}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-1\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-1\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-1\right)}}{2\times 8}$$

Multiply -32 times -1.

$$x=\frac{0±\sqrt{32}}{2\times 8}$$

Take the square root of 32.

$$x=\frac{0±4\sqrt{2}}{2\times 8}$$

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.

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