Chapter 9.4, Problem 67E

a.

To determine

To solve the equation with graphing method.

Answer to Problem 67E

Graph:

  

Explanation of Solution

Given:

Equation:

  $x^2+12x+2=12$

Calculation:

Converting the equation in standard form:

  $x^2+12x+2-12=0$

So,

  $x^2+12x-10=0$

On comparing the equation with $a{x}^2+bx+c$

  $a=1,b=12,c=-10$

Step:1 Finding the axis of symmetry.

  $x=\frac{-b}{2a}$

So,

  $x=\frac{-12}{2(1)}$

Therefore,

  $x=-6$

Step:2 $a=1$ , therefore $a>0$ so graph will open down.

Step:3

Find the plotting points:

  $y=x^2+12x-10$

For $x=-6$ find $y$

  $y={(-6)}^2+12(-6)-10$

So,

  $y=36-72-10$

So,

  $y=-46$

Again, for $x=-1$ find $y$

  $y={(-1)}^2+12(-1)-10$

So,

  $y=1-12-10$

So,

  $y=-21$

Again, for $y=-21$ find $y$

  $y={(1)}^2+12(1)-10$

So,

  $y=1+12-10$

So,

  $y=3$

Therefore plotting points are:

x	-1	-6	1
y	-21	-46	3

Plot the graph:

Plot all the points and axis of symmetry.

  

b.

To determine

To solve the equation with completing the square method.

Answer to Problem 67E

  $x=6+\sqrt{46}$ and $x=6-\sqrt{46}$

Explanation of Solution

Given:

Equation:

  $x^2+12x+2=12$

Calculation:

Converting the equation in standard form:

  $x^2+12x+2-12=0$

So,

  $x^2+12x-10=0$

Taking constant on one side

  $x^2+12x=10$

Taking square half of coefficient of $x$

i.e. ${(12\times \frac{1}{2})}^2$

so,

  ${(6)}^2=36$

Adding this on both side,

  $x^2+12x+36=10+36$

  $x^2+12x+36$ can be written as ${(x+6)}^2$

Therefore,

  ${(x+6)}^2=10+36$

Solving right hand side,

  ${(x+6)}^2=46$

So,

  $x+6=\pm \sqrt{46}$

Therefore ,

  $x=6\pm \sqrt{46}$

So,

  $x=6+\sqrt{46}$ and $x=6-\sqrt{46}$

c.

To determine

To determine which method is better.

Answer to Problem 67E

Completing the square method.

Explanation of Solution

Completing the square method is more preferable because it is easy and efficient.