Question

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:

If $a{x}^2+bx+c=0$, with role="math" localid="1649244506775" $a\ne 0$, then $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

$x^2+5x-6=0$

Short answer

The values of x are $\mathit{x}\mathbf{=}\mathbf{1}$and $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{6}$.

Step-by-step solution

Step 1. Understand the concept used.

If $a{x}^2+bx+c=0$, with $a\ne 0$, then $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$. Solving using factoring can be done by splitting the middle term of the equation and then making groups and equating them to zero.

Step 2. Substitute the values.

It is given that $x^2+5x-6=0$. Using the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 1 for $a,5$for $b$and $-6$for $c$.

Put the values in the formula and get.$x=\frac{-5\pm \sqrt{{\left(5\right)}^2-4\times \left(1\right)\times (-6)}}{2\left(1\right)}$

Step 3. Simplify for x.

Simplify the expression for $x$.

$x=\frac{-5\pm \sqrt{25-(-24)}}{2}$

$$\begin{gathered} =\frac{-5\pm \sqrt{25+24}}{2} \\ =\frac{-5\pm \sqrt{49}}{2} \\ =\frac{-5\pm 7}{2} \end{gathered}$$

Therefore, either $x=\frac{-5+7}{2}=\frac{2}{2}$or $x=\frac{-5-7}{2}=-\frac{12}{2}$that is., either$x=1$or $x=-6$.