Question

Solve by using the Quadratic Formula:$25t^2-40t=-16$

Short answer

The answer of the quadratic equation is$t=\frac{4}{5}$

Step-by-step solution

Given information

We are given a quadratic equation$25t^2-40t=-16$

identify the values of a,b,c

Firstly add $16$on both sides

we get, $25t^2-40t+16=0$

On comparing with standard equation we get$a=25,b=-40,c=16$

Write quadratic formula and substitute the values in it 

The quadratic formula can be given as

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

On substituting the values we get

$t=\frac{40\pm \sqrt{1600-4\left(25\right)\left(16\right)}}{2\left(25\right)}$

Simplify

On simplifying we have

$$\begin{gathered} t=\frac{40\pm \sqrt{1600-1600}}{50} \\ t=\frac{40}{50} \\ t=\frac{4}{5} \end{gathered}$$

Conclusion

The solution of the above quadratic equation is$t=\frac{4}{5}$