Question

What is the set of solutions of the equation x² + 3x – 4= 6?

Answer 1

$x^2+3x-4=6$

we need to set the equation equal to 0 to factor

$\begin{gathered} x^2+3x-4-6=0 \\ x^2+3x-10=0 \end{gathered}$

we can use this formula to factor

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

where a=1,b=3 and c=-10

$\begin{gathered} x=\frac{-(3)\pm\sqrt[]{(3)^2-4(1)(-10)}}{2(1)} \\ \\ x=\frac{-3\pm\sqrt[]{9+40}}{2} \\ \\ x=\frac{-3\pm\sqrt[]{49}}{2} \\ \\ x=\frac{-3\pm7}{2} \end{gathered}$

so, we have two solutions

$\begin{gathered} x_1=\frac{-3+7}{2} \\ x_1=\frac{4}{2} \\ x_1=2 \end{gathered}$$\begin{gathered} x_2=\frac{-3-7}{2} \\ x_2=\frac{-10}{2} \\ x_2=-5 \end{gathered}$

the two solutions are {-5,2}