Chapter 9.3, Problem 44E

a.

To determine

To solve: equation $x^2-12x+36=64$ without graphing.

Answer to Problem 44E

The required answer is: the roots are $x=-2$ and $x=14$

Explanation of Solution

Given information:

The given equation: $x^2-12x+36=64$

Calculation:

  $\begin{array}{l}{x}^2-12x+36=64\\ x^2-12x+36-64=64-64\end{array}$

(Subtract 64 from both sides)

  $x^2-12x-28=0$

(Simplify)

  $\begin{array}{l}{x}^2-14x+2x-28=0\\ x(x-14)+2(x-14)=0\\ (x+2)(x-14)=0\end{array}$

(Factor $x^2-12x-28$ )

  $x+2=0$ Or $x-14=0$

(Zero product property)

  $x=-2$ Or $x=14$

(Solve for x)

Therefore, the roots are $x=-2$ and $x=14$

b.

To determine

To solve: equation $x^2+14x+49=16$ without graphing.

Answer to Problem 44E

The required answer is: the roots are $x=-3$ and $x=-11$

Explanation of Solution

Given information:

The given equation: $x^2+14x+49=16$

Calculation:

  $\begin{array}{l}{x}^2+14x+49=16\\ x^2+14x+49-16=16-16\end{array}$

(Subtract 16 from both sides)

  $x^2+14x+33=0$

(Simplify)

  $\begin{array}{l}{x}^2+11x+3x+33=0\\ x(x+11)+3(x+11)=0\\ (x+3)(x+11)=0\end{array}$

(Factor $x^2+14x+33$ )

  $x+3=0$ Or $x+11=0$

(Zero product property)

  $x=-3$ Or $x=-11$

(Solve for x)

Therefore, the roots are $x=-3$ and $x=-11$