Question

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

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

$x(x+5)=14$

Short answer

The values of x are$x=2$and$x=-7$ .

Step-by-step solution

- 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 equation and then making groups and equating them to zero.

- Substitute the values 

It is given that $x(x+5)=14$which can also be written as . Using quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 1 for a, 5 for b and -14 for c. Put the values in the formula and get $x=\frac{-5\pm \sqrt{{\left(5\right)}^2-4\times \left(1\right)\times \left(-14\right)}}{2\left(1\right)}$.

- Simplify for x 

Simplify the expression for x.

$\begin{array}{c}x=\frac{-5\pm \sqrt{{\left(5\right)}^2-4\times \left(1\right)\times \left(-14\right)}}{2\left(1\right)}\\ =\frac{-5\pm \sqrt{25+56}}{2}\\ =\frac{-5\pm \sqrt{81}}{2}\\ =\frac{-5\pm 9}{2}\end{array}$

Therefore, either $x=\frac{-5+9}{2}=\frac{4}{2}$or $x=\frac{-5-9}{2}=-\frac{14}{2}$that is., either$x=2$ or$x=-7$ .