Solve 2x^2-39-412=0

$$2 x ^ { 2 } - 39 - 412 = 0$$

Solve for x

$$x = \frac{\sqrt{902}}{2} \approx 15.016657418$$

$$x = -\frac{\sqrt{902}}{2} \approx -15.016657418$$

Steps by Finding Square Root

Subtract 412 from -39 to get -451.

$$2x^{2}-451=0$$

Add 451 to both sides. Anything plus zero gives itself.

$$2x^{2}=451$$

Divide both sides by 2.

$$x^{2}=\frac{451}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{902}}{2} x=-\frac{\sqrt{902}}{2}$$

Steps Using the Quadratic Formula

Subtract 412 from -39 to get -451.

$$2x^{2}-451=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -451 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-451\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-451\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-451\right)}}{2\times 2}$$

Multiply -8 times -451.

$$x=\frac{0±\sqrt{3608}}{2\times 2}$$

Take the square root of 3608.

$$x=\frac{0±2\sqrt{902}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{902}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{902}}{4} when ± is plus.

$$x=\frac{\sqrt{902}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{902}}{4} when ± is minus.

$$x=-\frac{\sqrt{902}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{902}}{2} x=-\frac{\sqrt{902}}{2}$$