Chapter 4, Problem 3AR

To determine

To Solve: The quadratic equation $y^2-7y-18=0$ using factoring or quadratic formula.

Answer to Problem 3AR

The solution of equation is either $y=9$ or $y=-2$

Explanation of Solution

Given information:

The quadratic equation $y^2-7y-18=0$

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

  $y^2-7y-18=0$

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

Where $a=1,b=-7\&c=-18$

Putting the values in the formula

  $\begin{array}{l}y=\frac{-\left(-7\right)\pm \sqrt{{\left(-7\right)}^2-4\times \left(1\right)\times \left(-18\right)}}{2\left(1\right)}\\ y=\frac{7\pm \sqrt{49-\left(-72\right)}}{2}\\ y=\frac{7\pm \sqrt{121}}{2}\\ y=\frac{7\pm 11}{2}\end{array}$

Therefore either $y=\frac{7+11}{2}=\frac{18}{2}$ or $y=\frac{7-11}{2}=-\frac{4}{2}$

Either $y=9$ or $y=-2$

Conclusion:

The solution of equation is either $y=9$ or $y=-2$