Solve 3x^2+8=72

$$3 { x }^{ 2 } +8 = 72$$

Solve for x

$$x = \frac{8 \sqrt{3}}{3} \approx 4.618802154$$

$$x = -\frac{8 \sqrt{3}}{3} \approx -4.618802154$$

Steps by Finding Square Root

Subtract 8 from both sides.

$$3x^{2}=72-8$$

Subtract 8 from 72 to get 64.

$$3x^{2}=64$$

Divide both sides by 3.

$$x^{2}=\frac{64}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{8\sqrt{3}}{3} x=-\frac{8\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Subtract 72 from both sides.

$$3x^{2}+8-72=0$$

Subtract 72 from 8 to get -64.

$$3x^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-64\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-64\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-64\right)}}{2\times 3}$$

Multiply -12 times -64.

$$x=\frac{0±\sqrt{768}}{2\times 3}$$

Take the square root of 768.

$$x=\frac{0±16\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±16\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±16\sqrt{3}}{6} when ± is plus.

$$x=\frac{8\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±16\sqrt{3}}{6} when ± is minus.

$$x=-\frac{8\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{8\sqrt{3}}{3} x=-\frac{8\sqrt{3}}{3}$$