Solve 48-2x^2=0

$$48-2 { x }^{ 2 } =0$$

Solve for x

$$x=2\sqrt{6}\approx 4.898979486$$

$$x=-2\sqrt{6}\approx -4.898979486$$

Steps by Finding Square Root

Subtract 48 from both sides. Anything subtracted from zero gives its negation.

$$-2x^{2}=-48$$

Divide both sides by -2.

$$x^{2}=\frac{-48}{-2}$$

Divide -48 by -2 to get 24.

$$x^{2}=24$$

Take the square root of both sides of the equation.

$$x=2\sqrt{6} x=-2\sqrt{6}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-2x^{2}+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 48}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 48}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 48}}{2\left(-2\right)}$$

Multiply 8 times 48.

$$x=\frac{0±\sqrt{384}}{2\left(-2\right)}$$

Take the square root of 384.

$$x=\frac{0±8\sqrt{6}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±8\sqrt{6}}{-4}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{-4} when ± is plus.

$$x=-2\sqrt{6}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{-4} when ± is minus.

$$x=2\sqrt{6}$$

The equation is now solved.

$$x=-2\sqrt{6} x=2\sqrt{6}$$