Identify the values of a, b, and c, by comparing the given equation to the following.
[tex]ax^2+bx+c=0[/tex]
Thus, the value of a, b, and c are as follows.
[tex]\begin{gathered} a=2 \\ b=7 \\ c=5 \end{gathered}[/tex]
Substitute the values into the quadratic formula.
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-7\pm\sqrt[]{7^2-4(2)(5)}}{2(2)} \end{gathered}[/tex]
Simplify the exponential expression.
[tex]x=\frac{-7\pm\sqrt[]{49^{}-4(2)(5)}}{2(2)}[/tex]
Multiply.
[tex]x=\frac{-7\pm\sqrt[]{49^{}-40}}{4}[/tex]
Subtract.
[tex]x=\frac{-7\pm\sqrt[]{9}}{4}[/tex]
Evaluate the radical expression.
[tex]x=\frac{-7\pm3}{4}[/tex]
Rewrite the equation in two separate equations.
[tex]\begin{gathered} x=\frac{-7+3}{4} \\ \\ x=\frac{-7-3}{4} \end{gathered}[/tex]
Simplify the numerators.
[tex]\begin{gathered} x=\frac{-7+3}{4}=\frac{-4}{4}=-1 \\ \\ x=\frac{-7-3}{4}=-\frac{10}{4}=-\frac{5}{2} \end{gathered}[/tex]
Thus,
[tex]x=-1,-\frac{5}{2}[/tex]
