Question

Solve the equation using quadratic formula.

$25t^2-40t=-16$

Short answer

The roots are$t=\frac{4}{5}$.

Step-by-step solution

 Given Information.  

The given equation is $25t^2-40t=-16$.

Write the quadratic equation in standard form and identify  a,b,c.

$25t^2-40t=-16$

Rewrite in standard form.

$25t^2-40t+16=0$

Here,

$a=25,b=-40,c=16$

Substitute the values in quadratic formula.

$$\begin{gathered} t=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ t=\frac{-(-40)\pm \sqrt{(-40{)}^2-4(25\left)\right(16)}}{2\left(25\right)} \\ t=\frac{40\pm \sqrt{1600-1600}}{50} \\ t=\frac{40\pm \sqrt{0}}{50} \end{gathered}$$

The square root of zero is zero itself.

So,

$$\begin{gathered} t=\frac{40}{50} \\ t=\frac{4}{5} \end{gathered}$$

The root is$t=\frac{4}{5}$.