Solve (-5t)^2=255^2/36

$$( - 5 t ) ^ { 2 } = \frac { 255 ^ { 2 } } { 36 }$$

Solve for t

$$t = -\frac{17}{2} = -8\frac{1}{2} = -8.5$$

$$t = \frac{17}{2} = 8\frac{1}{2} = 8.5$$

Steps Using Difference of Squares

Multiply both sides of the equation by 36.

$$36\left(-5t\right)^{2}=255^{2}$$

Expand \left(-5t\right)^{2}.

$$36\left(-5\right)^{2}t^{2}=255^{2}$$

Calculate -5 to the power of 2 and get 25.

$$36\times 25t^{2}=255^{2}$$

Multiply 36 and 25 to get 900.

$$900t^{2}=255^{2}$$

Calculate 255 to the power of 2 and get 65025.

$$900t^{2}=65025$$

Subtract 65025 from both sides.

$$900t^{2}-65025=0$$

Divide both sides by 225.

$$4t^{2}-289=0$$

Consider 4t^{2}-289. Rewrite 4t^{2}-289 as \left(2t\right)^{2}-17^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2t-17\right)\left(2t+17\right)=0$$

To find equation solutions, solve 2t-17=0 and 2t+17=0.

$$t=\frac{17}{2} t=-\frac{17}{2}$$

Steps by Finding Square Root

Multiply both sides of the equation by 36.

$$36\left(-5t\right)^{2}=255^{2}$$

Expand \left(-5t\right)^{2}.

$$36\left(-5\right)^{2}t^{2}=255^{2}$$

Calculate -5 to the power of 2 and get 25.

$$36\times 25t^{2}=255^{2}$$

Multiply 36 and 25 to get 900.

$$900t^{2}=255^{2}$$

Calculate 255 to the power of 2 and get 65025.

$$900t^{2}=65025$$

Divide both sides by 900.

$$t^{2}=\frac{65025}{900}$$

Reduce the fraction \frac{65025}{900} to lowest terms by extracting and canceling out 225.

$$t^{2}=\frac{289}{4}$$

Take the square root of both sides of the equation.

$$t=\frac{17}{2} t=-\frac{17}{2}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 36.

$$36\left(-5t\right)^{2}=255^{2}$$

Expand \left(-5t\right)^{2}.

$$36\left(-5\right)^{2}t^{2}=255^{2}$$

Calculate -5 to the power of 2 and get 25.

$$36\times 25t^{2}=255^{2}$$

Multiply 36 and 25 to get 900.

$$900t^{2}=255^{2}$$

Calculate 255 to the power of 2 and get 65025.

$$900t^{2}=65025$$

Subtract 65025 from both sides.

$$900t^{2}-65025=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 900 for a, 0 for b, and -65025 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 900\left(-65025\right)}}{2\times 900}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 900\left(-65025\right)}}{2\times 900}$$

Multiply -4 times 900.

$$t=\frac{0±\sqrt{-3600\left(-65025\right)}}{2\times 900}$$

Multiply -3600 times -65025.

$$t=\frac{0±\sqrt{234090000}}{2\times 900}$$

Take the square root of 234090000.

$$t=\frac{0±15300}{2\times 900}$$

Multiply 2 times 900.

$$t=\frac{0±15300}{1800}$$

Now solve the equation t=\frac{0±15300}{1800} when ± is plus. Reduce the fraction \frac{15300}{1800} to lowest terms by extracting and canceling out 900.

$$t=\frac{17}{2}$$

Now solve the equation t=\frac{0±15300}{1800} when ± is minus. Reduce the fraction \frac{-15300}{1800} to lowest terms by extracting and canceling out 900.

$$t=-\frac{17}{2}$$

The equation is now solved.

$$t=\frac{17}{2} t=-\frac{17}{2}$$