Question

Solve the equation using quadratic formula.

$5m^2+2m-7=0$

Short answer

The roots are$m=\frac{-7}{5},m=1$.

Step-by-step solution

 Given Information.   

The given equation is$5m^2+2m-7=0$.

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

$5m^2+2m-7=0$

The equation is in standard form.

So,

$a=5,b=2,c=-7$.

Substitute the values in quadratic formula.  

$$\begin{gathered} m=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ m=\frac{-2\pm \sqrt{2^2-4\left(5\right)(-7)}}{2\left(5\right)} \\ m=\frac{-2\pm \sqrt{4+140}}{10} \\ m=\frac{-2\pm \sqrt{144}}{10} \end{gathered}$$

Use square root property.

$m=\frac{-2\pm 12}{10}$

Rewrite to show two solutions.

$$\begin{gathered} m_1=\frac{-2+12}{10} \\ {m}_1=\frac{10}{10} \\ {m}_1=1 \end{gathered}$$

and

$$\begin{gathered} m_2=\frac{-2-12}{10} \\ {m}_2=\frac{-14}{10} \\ {m}_2=\frac{-7}{5} \end{gathered}$$

Thus, the roots are$m=\frac{-7}{5},m=1$.