Solve 25=8t^2/2

$$25 = \frac { 8 t ^ { 2 } } { 2 }$$

Solve for t

$$t = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$t = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps Using Difference of Squares

Multiply both sides by 2.

$$25\times 2=8t^{2}$$

Multiply 25 and 2 to get 50.

$$50=8t^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$8t^{2}=50$$

Subtract 50 from both sides.

$$8t^{2}-50=0$$

Divide both sides by 2.

$$4t^{2}-25=0$$

Consider 4t^{2}-25. Rewrite 4t^{2}-25 as \left(2t\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2t-5\right)\left(2t+5\right)=0$$

To find equation solutions, solve 2t-5=0 and 2t+5=0.

$$t=\frac{5}{2} t=-\frac{5}{2}$$

Steps by Finding Square Root

Multiply both sides by 2.

$$25\times 2=8t^{2}$$

Multiply 25 and 2 to get 50.

$$50=8t^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$8t^{2}=50$$

Divide both sides by 8.

$$t^{2}=\frac{50}{8}$$

Reduce the fraction \frac{50}{8} to lowest terms by extracting and canceling out 2.

$$t^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$t=\frac{5}{2} t=-\frac{5}{2}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$25\times 2=8t^{2}$$

Multiply 25 and 2 to get 50.

$$50=8t^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$8t^{2}=50$$

Subtract 50 from both sides.

$$8t^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 8\left(-50\right)}}{2\times 8}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 8\left(-50\right)}}{2\times 8}$$

Multiply -4 times 8.

$$t=\frac{0±\sqrt{-32\left(-50\right)}}{2\times 8}$$

Multiply -32 times -50.

$$t=\frac{0±\sqrt{1600}}{2\times 8}$$

Take the square root of 1600.

$$t=\frac{0±40}{2\times 8}$$

Multiply 2 times 8.

$$t=\frac{0±40}{16}$$

Now solve the equation t=\frac{0±40}{16} when ± is plus. Reduce the fraction \frac{40}{16} to lowest terms by extracting and canceling out 8.

$$t=\frac{5}{2}$$

Now solve the equation t=\frac{0±40}{16} when ± is minus. Reduce the fraction \frac{-40}{16} to lowest terms by extracting and canceling out 8.

$$t=-\frac{5}{2}$$

The equation is now solved.

$$t=\frac{5}{2} t=-\frac{5}{2}$$