Solve 8x^2+6=22

$$8 x ^ { 2 } + 6 = 22$$

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Subtract 6 from both sides.

$$8x^{2}=22-6$$

Subtract 6 from 22 to get 16.

$$8x^{2}=16$$

Divide both sides by 8.

$$x^{2}=\frac{16}{8}$$

Divide 16 by 8 to get 2.

$$x^{2}=2$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 22 from both sides.

$$8x^{2}+6-22=0$$

Subtract 22 from 6 to get -16.

$$8x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-16\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-16\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-16\right)}}{2\times 8}$$

Multiply -32 times -16.

$$x=\frac{0±\sqrt{512}}{2\times 8}$$

Take the square root of 512.

$$x=\frac{0±16\sqrt{2}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±16\sqrt{2}}{16}$$

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

$$x=\sqrt{2}$$

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

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

The equation is now solved.

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