Solve 8x^2+72=216

$$8 x ^ { 2 } + 72 = 216$$

Solve for x

$$x=3\sqrt{2}\approx 4.242640687$$

$$x=-3\sqrt{2}\approx -4.242640687$$

Steps by Finding Square Root

Subtract 72 from both sides.

$$8x^{2}=216-72$$

Subtract 72 from 216 to get 144.

$$8x^{2}=144$$

Divide both sides by 8.

$$x^{2}=\frac{144}{8}$$

Divide 144 by 8 to get 18.

$$x^{2}=18$$

Take the square root of both sides of the equation.

$$x=3\sqrt{2} x=-3\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 216 from both sides.

$$8x^{2}+72-216=0$$

Subtract 216 from 72 to get -144.

$$8x^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-144\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-144\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-144\right)}}{2\times 8}$$

Multiply -32 times -144.

$$x=\frac{0±\sqrt{4608}}{2\times 8}$$

Take the square root of 4608.

$$x=\frac{0±48\sqrt{2}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±48\sqrt{2}}{16}$$

Now solve the equation x=\frac{0±48\sqrt{2}}{16} when ± is plus.

$$x=3\sqrt{2}$$

Now solve the equation x=\frac{0±48\sqrt{2}}{16} when ± is minus.

$$x=-3\sqrt{2}$$

The equation is now solved.

$$x=3\sqrt{2} x=-3\sqrt{2}$$