Solve t^2=9^3/900

$$t ^ { 2 } = \frac { 9 ^ { 3 } } { 900 }$$

Solve for t

$$t=\frac{9}{10}=0.9$$

$$t=-\frac{9}{10}=-0.9$$

Steps Using Difference of Squares

Multiply both sides of the equation by 900.

$$900t^{2}=9^{3}$$

Calculate 9 to the power of 3 and get 729.

$$900t^{2}=729$$

Subtract 729 from both sides.

$$900t^{2}-729=0$$

Divide both sides by 9.

$$100t^{2}-81=0$$

Consider 100t^{2}-81. Rewrite 100t^{2}-81 as \left(10t\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(10t-9\right)\left(10t+9\right)=0$$

To find equation solutions, solve 10t-9=0 and 10t+9=0.

$$t=\frac{9}{10} t=-\frac{9}{10}$$

Steps by Finding Square Root

Multiply both sides of the equation by 900.

$$900t^{2}=9^{3}$$

Calculate 9 to the power of 3 and get 729.

$$900t^{2}=729$$

Divide both sides by 900.

$$t^{2}=\frac{729}{900}$$

Reduce the fraction \frac{729}{900} to lowest terms by extracting and canceling out 9.

$$t^{2}=\frac{81}{100}$$

Take the square root of both sides of the equation.

$$t=\frac{9}{10} t=-\frac{9}{10}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 900.

$$900t^{2}=9^{3}$$

Calculate 9 to the power of 3 and get 729.

$$900t^{2}=729$$

Subtract 729 from both sides.

$$900t^{2}-729=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 900 for a, 0 for b, and -729 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 900\left(-729\right)}}{2\times 900}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 900\left(-729\right)}}{2\times 900}$$

Multiply -4 times 900.

$$t=\frac{0±\sqrt{-3600\left(-729\right)}}{2\times 900}$$

Multiply -3600 times -729.

$$t=\frac{0±\sqrt{2624400}}{2\times 900}$$

Take the square root of 2624400.

$$t=\frac{0±1620}{2\times 900}$$

Multiply 2 times 900.

$$t=\frac{0±1620}{1800}$$

Now solve the equation t=\frac{0±1620}{1800} when ± is plus. Reduce the fraction \frac{1620}{1800} to lowest terms by extracting and canceling out 180.

$$t=\frac{9}{10}$$

Now solve the equation t=\frac{0±1620}{1800} when ± is minus. Reduce the fraction \frac{-1620}{1800} to lowest terms by extracting and canceling out 180.

$$t=-\frac{9}{10}$$

The equation is now solved.

$$t=\frac{9}{10} t=-\frac{9}{10}$$