Question

Problem 1:Solve using the Quadratic Formula method: 5x^2 + 7x + 2 = 0Problem 2:Solve: x2 + 2x + 7 = 0

Answer 1

The Solution to problem 1:

Given the quadratic equation below:

$5x^2+7x+2=0$

We are required to solve using the Formula method.

Step 1:

The quadratic formula is given as below:

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

in this case,

$\begin{gathered} a=5 \\ b=7 \\ c=2 \end{gathered}$

Step 2:

Substituting these values in the formula above, we get

$x=\frac{-(7)\pm\sqrt[]{7^2-4(5)(2)}}{2(5)}$$x=\frac{-7\pm\sqrt[]{49^{}-40}}{10}=\frac{-7\pm\text{ }\sqrt[]{9}}{10}=\frac{-7\pm3}{10}$$\begin{gathered} x=\frac{-7-3}{10}\text{ or x= }\frac{-7+3}{10} \\ \\ x=-\frac{10}{10}\text{ or x=}\frac{-4}{10} \\ \\ c=-1\text{ or x=}\frac{-2}{5} \end{gathered}$

Therefore, the solution problem 1 is:

$x=-1\text{ or x =-}\frac{2}{5}$