Chapter 1.3, Problem 28AYU

In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$x^2-7x-18=0$

To determine

To find: The solution for the equation $x^2\text{ − 7}x\text{ − 18 = 0}$ algebraically and verify using a graphing utility.

Answer to Problem 28AYU

Solution:

$x\text{ = − 4 , 7}$

Explanation of Solution

Given:

The equation $x^2\text{ − 7}x\text{ − 18 = 0}$

Algebraic solution:

$x^2\text{ − 7}x\text{ − 18 = 0}$

$x^2 -\text{ 9}x+2x-18=0$Splitting the middle term

$x\left(x\text{ − 9}\right)\text{ + 2}\left(x\text{ − 9}\right)\text{ = 0}$Taking common factor $x$ from first two terms and 2 from next two term

$\left(x\text{ − 9}\right)\left(x\text{ + 2}\right)\text{ = 0}$

$x\text{ − 9 = 0}$ or $x\text{ + 2 = 0}$

$x\text{ = 9}$ or $x\text{ = − 2}$

Check:

Let $x\text{ = 9}$ in the expression in $x$ on the left side of the equation

${(9)}^2 -7\left(9\right)-18$

$\text{= 81 − 63 − 18}$

$\text{= 81 − 81 = 0}$

Let$x\text{ = −2}$ in the expression in $x$ on the right side of the equation

${\text{(−2)}}^{\text{2}}\text{ − 7}\left(\text{−2}\right)\text{ − 18}$

$\text{= 4 + 14 − 18}$

$=18-18$

$=0$

Since the two expressions are equal, the solution $x\text{ = −2, 9}$ checks.