Solve 16=80/x^2

$$16 = \frac { 80 } { x ^ { 2 } }$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

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}.

$$16x^{2}=80$$

Divide both sides by 16.

$$x^{2}=\frac{80}{16}$$

Divide 80 by 16 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

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

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}.

$$16x^{2}=80$$

Subtract 80 from both sides.

$$16x^{2}-80=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-80\right)}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-80\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\left(-80\right)}}{2\times 16}$$

Multiply -64 times -80.

$$x=\frac{0±\sqrt{5120}}{2\times 16}$$

Take the square root of 5120.

$$x=\frac{0±32\sqrt{5}}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±32\sqrt{5}}{32}$$

Now solve the equation x=\frac{0±32\sqrt{5}}{32} when ± is plus.

$$x=\sqrt{5}$$

Now solve the equation x=\frac{0±32\sqrt{5}}{32} when ± is minus.

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

The equation is now solved.

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