Chapter 9.4, Problem 36E

To determine

To describe first step in solve the equation by complete the square for expression.

  $3x^2+6x=12$

Answer to Problem 36E

The solutions are $-1+\sqrt{5}$ and $-1-\sqrt{5}$

Explanation of Solution

Given information:

Expression

  $3x^2+6x=12$

Calculation:

Original equation

  $3x^2+6x=12$

First step

  $a\ne 1$

Then

Divide by $3$ both sides to make $a=1$

  $\frac{3x^2+6x}{3}=\frac{12}{3}$

On solving

  $x^2+2x=4$

Since ${\left(\frac{2}{2}\right)}^2=1$ , add $1$ to both sides

  $x^2+2x+1=5$

Factor $x^2+2x+1$

  ${(x+1)}^2=5$

On solving

  $x+1=\pm \sqrt{5}$

Subtract $1$ both sides

  $x=-1\pm \sqrt{5}$

Separating the equations

  $x=-1+\sqrt{5}$ Or $x=-1-\sqrt{5}$

The solutions are $-1+\sqrt{5}$ and $-1-\sqrt{5}$