Solve 1/2x^2=40

$$1 / 2 x ^ { 2 } = 40$$

Solve for x

$$x=4\sqrt{5}\approx 8.94427191$$

$$x=-4\sqrt{5}\approx -8.94427191$$

Steps by Finding Square Root

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x^{2}=40\times 2$$

Multiply 40 and 2 to get 80.

$$x^{2}=80$$

Take the square root of both sides of the equation.

$$x=4\sqrt{5} x=-4\sqrt{5}$$

Steps Using the Quadratic Formula

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x^{2}=40\times 2$$

Multiply 40 and 2 to get 80.

$$x^{2}=80$$

Subtract 80 from both sides.

$$x^{2}-80=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-80\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-80\right)}}{2}$$

Multiply -4 times -80.

$$x=\frac{0±\sqrt{320}}{2}$$

Take the square root of 320.

$$x=\frac{0±8\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{5}}{2} when ± is plus.

$$x=4\sqrt{5}$$

Now solve the equation x=\frac{0±8\sqrt{5}}{2} when ± is minus.

$$x=-4\sqrt{5}$$

The equation is now solved.

$$x=4\sqrt{5} x=-4\sqrt{5}$$