Solve 2-40/x^2=0

$$2- \frac{ 40 }{ { x }^{ 2 } } = 0$$

Solve for x

$$x=2\sqrt{5}\approx 4.472135955$$

$$x=-2\sqrt{5}\approx -4.472135955$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$x^{2}\times 2-40=0$$

Add 40 to both sides. Anything plus zero gives itself.

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

Divide both sides by 2.

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

Divide 40 by 2 to get 20.

$$x^{2}=20$$

Take the square root of both sides of the equation.

$$x=2\sqrt{5} x=-2\sqrt{5}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$x^{2}\times 2-40=0$$

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.

$$2x^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-40\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-40\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-40\right)}}{2\times 2}$$

Multiply -8 times -40.

$$x=\frac{0±\sqrt{320}}{2\times 2}$$

Take the square root of 320.

$$x=\frac{0±8\sqrt{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8\sqrt{5}}{4}$$

Now solve the equation x=\frac{0±8\sqrt{5}}{4} when ± is plus.

$$x=2\sqrt{5}$$

Now solve the equation x=\frac{0±8\sqrt{5}}{4} when ± is minus.

$$x=-2\sqrt{5}$$

The equation is now solved.

$$x=2\sqrt{5} x=-2\sqrt{5}$$