Solve 100=36/d^2

$$100 = \frac { 36 } { d ^ { 2 } }$$

Solve for d

$$d=\frac{3}{5}=0.6$$

$$d=-\frac{3}{5}=-0.6$$

Steps Using Difference of Squares

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

$$100d^{2}=36$$

Subtract 36 from both sides.

$$100d^{2}-36=0$$

Divide both sides by 4.

$$25d^{2}-9=0$$

Consider 25d^{2}-9. Rewrite 25d^{2}-9 as \left(5d\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5d-3\right)\left(5d+3\right)=0$$

To find equation solutions, solve 5d-3=0 and 5d+3=0.

$$d=\frac{3}{5} d=-\frac{3}{5}$$

Steps by Finding Square Root

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

$$100d^{2}=36$$

Divide both sides by 100.

$$d^{2}=\frac{36}{100}$$

Reduce the fraction \frac{36}{100} to lowest terms by extracting and canceling out 4.

$$d^{2}=\frac{9}{25}$$

Take the square root of both sides of the equation.

$$d=\frac{3}{5} d=-\frac{3}{5}$$

Steps Using the Quadratic Formula

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

$$100d^{2}=36$$

Subtract 36 from both sides.

$$100d^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\times 100\left(-36\right)}}{2\times 100}$$

Square 0.

$$d=\frac{0±\sqrt{-4\times 100\left(-36\right)}}{2\times 100}$$

Multiply -4 times 100.

$$d=\frac{0±\sqrt{-400\left(-36\right)}}{2\times 100}$$

Multiply -400 times -36.

$$d=\frac{0±\sqrt{14400}}{2\times 100}$$

Take the square root of 14400.

$$d=\frac{0±120}{2\times 100}$$

Multiply 2 times 100.

$$d=\frac{0±120}{200}$$

Now solve the equation d=\frac{0±120}{200} when ± is plus. Reduce the fraction \frac{120}{200} to lowest terms by extracting and canceling out 40.

$$d=\frac{3}{5}$$

Now solve the equation d=\frac{0±120}{200} when ± is minus. Reduce the fraction \frac{-120}{200} to lowest terms by extracting and canceling out 40.

$$d=-\frac{3}{5}$$

The equation is now solved.

$$d=\frac{3}{5} d=-\frac{3}{5}$$