Solve 0.05=5t^2-1.25

$$0.05 = 5 { t }^{ 2 } -1.25$$

Solve for t

$$t=\frac{\sqrt{26}}{10}\approx 0.509901951$$

$$t=-\frac{\sqrt{26}}{10}\approx -0.509901951$$

Steps by Finding Square Root

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

$$5t^{2}-1.25=0.05$$

Add 1.25 to both sides.

$$5t^{2}=0.05+1.25$$

Add 0.05 and 1.25 to get 1.3.

$$5t^{2}=1.3$$

Divide both sides by 5.

$$t^{2}=\frac{1.3}{5}$$

Expand \frac{1.3}{5} by multiplying both numerator and the denominator by 10.

$$t^{2}=\frac{13}{50}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{26}}{10} t=-\frac{\sqrt{26}}{10}$$

Steps Using the Quadratic Formula

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

$$5t^{2}-1.25=0.05$$

Subtract 0.05 from both sides.

$$5t^{2}-1.25-0.05=0$$

Subtract 0.05 from -1.25 to get -1.3.

$$5t^{2}-1.3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -1.3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 5\left(-1.3\right)}}{2\times 5}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 5\left(-1.3\right)}}{2\times 5}$$

Multiply -4 times 5.

$$t=\frac{0±\sqrt{-20\left(-1.3\right)}}{2\times 5}$$

Multiply -20 times -1.3.

$$t=\frac{0±\sqrt{26}}{2\times 5}$$

Multiply 2 times 5.

$$t=\frac{0±\sqrt{26}}{10}$$

Now solve the equation t=\frac{0±\sqrt{26}}{10} when ± is plus.

$$t=\frac{\sqrt{26}}{10}$$

Now solve the equation t=\frac{0±\sqrt{26}}{10} when ± is minus.

$$t=-\frac{\sqrt{26}}{10}$$

The equation is now solved.

$$t=\frac{\sqrt{26}}{10} t=-\frac{\sqrt{26}}{10}$$