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=(-3\pm7)/(2) \end{gathered}`

so, we have two solutions

`\begin{gathered} x_1=(-3+7)/(2) \\ x_1=(4)/(2) \\ x_1=2 \end{gathered}`
`\begin{gathered} x_2=(-3-7)/(2) \\ x_2=(-10)/(2) \\ x_2=-5 \end{gathered}`

the two solutions are {-5,2}