Chapter 4, Problem 4AR

To determine

To Solve: The quadratic equation $x^2+8x=0$ using factoring or quadratic formula.

Answer to Problem 4AR

The solution of equation is either $x=8$ or $x=0$ .

Explanation of Solution

Given information:

The quadratic equation $x^2+8x=0$

Concept and Formula Used:

Quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ where quadratic equation is $a{x}^2+bx+c=0$

Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

Calculation:

It is given that

  $x^2+8x=0$

Solving equation using quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Where $a=1,b=8\&c=0$

Putting the values in the formula

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

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

Either $x=8$ or $x=0$

Conclusion:

The solution of equation is either $x=8$ or $x=0$ .