Solve 2x^2+4=72

$$2 x ^ { 2 } + 4 = 72$$

Solve for x

$$x=\sqrt{34}\approx 5.830951895$$

$$x=-\sqrt{34}\approx -5.830951895$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$2x^{2}=72-4$$

Subtract 4 from 72 to get 68.

$$2x^{2}=68$$

Divide both sides by 2.

$$x^{2}=\frac{68}{2}$$

Divide 68 by 2 to get 34.

$$x^{2}=34$$

Take the square root of both sides of the equation.

$$x=\sqrt{34} x=-\sqrt{34}$$

Steps Using the Quadratic Formula

Subtract 72 from both sides.

$$2x^{2}+4-72=0$$

Subtract 72 from 4 to get -68.

$$2x^{2}-68=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -68 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-68\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-68\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-68\right)}}{2\times 2}$$

Multiply -8 times -68.

$$x=\frac{0±\sqrt{544}}{2\times 2}$$

Take the square root of 544.

$$x=\frac{0±4\sqrt{34}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{34}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{34}}{4} when ± is plus.

$$x=\sqrt{34}$$

Now solve the equation x=\frac{0±4\sqrt{34}}{4} when ± is minus.

$$x=-\sqrt{34}$$

The equation is now solved.

$$x=\sqrt{34} x=-\sqrt{34}$$