Answer
$x=\left\{ -7,4 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the solutions of the given equation, $
x^2+3x-28=0
,$ use the Quadratic Formula.
$\bf{\text{Solution Details:}}$
Using the form $ax^2+bx+c=0,$ the quadratic equation above has $a=
1
, b=
3
, c=
-28
.$ Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, then
\begin{array}{l}\require{cancel}
x=\dfrac{-3\pm\sqrt{3^2-4(1)(-28)}}{2(1)}
\\\\
x=\dfrac{-3\pm\sqrt{9+112}}{2}
\\\\
x=\dfrac{-3\pm\sqrt{121}}{2}
\\\\
x=\dfrac{-3\pm11}{2}
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
x=\dfrac{-3-11}{2}
\\\\
x=\dfrac{-14}{2}
\\\\
x=-7
\\\\\text{OR}\\\\
x=\dfrac{-3+11}{2}
\\\\
x=\dfrac{8}{2}
\\\\
x=4
.\end{array}
Hence, $
x=\left\{ -7,4 \right\}
.$
