Solve 8x^2-3=2

$$8 x ^ { 2 } - 3 = 2$$

Solve for x

$$x=\frac{\sqrt{10}}{4}\approx 0.790569415$$

$$x=-\frac{\sqrt{10}}{4}\approx -0.790569415$$

Steps by Finding Square Root

Add 3 to both sides.

$$8x^{2}=2+3$$

Add 2 and 3 to get 5.

$$8x^{2}=5$$

Divide both sides by 8.

$$x^{2}=\frac{5}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{4} x=-\frac{\sqrt{10}}{4}$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$8x^{2}-3-2=0$$

Subtract 2 from -3 to get -5.

$$8x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-5\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-5\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-5\right)}}{2\times 8}$$

Multiply -32 times -5.

$$x=\frac{0±\sqrt{160}}{2\times 8}$$

Take the square root of 160.

$$x=\frac{0±4\sqrt{10}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±4\sqrt{10}}{16}$$

Now solve the equation x=\frac{0±4\sqrt{10}}{16} when ± is plus.

$$x=\frac{\sqrt{10}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{10}}{16} when ± is minus.

$$x=-\frac{\sqrt{10}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{4} x=-\frac{\sqrt{10}}{4}$$