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

$x^2+8x=0$

Short answer

The values of x are$x=-8$ and$x=0$.

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$x^2+8x=0$.Using quadratic formula$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 1 for a, 8 for b and 0 for c.

Put the values in the formula and get$x=\frac{-8\pm \sqrt{{\left(8\right)}^2-4\times \left(1\right)\times \left(0\right)}}{2\left(1\right)}$.

- Simplify for x 

Simplify the expression for x.

$\begin{array}{c}x=\frac{-\left(8\right)\pm \sqrt{{\left(8\right)}^2-4\times \left(1\right)\times \left(0\right)}}{2\left(1\right)}\\ =\frac{-8\pm \sqrt{64-0}}{2}\\ =\frac{-8\pm \sqrt{64}}{2}\\ =\frac{-8\pm 8}{2}\end{array}$

Therefore, either $x=\frac{-8+8}{2}=\frac{0}{2}$or$x=\frac{-8-8}{2}=\frac{-16}{2}$ that is., either x=0 or x=-8.