Chapter 9.4, Problem 28E

To determine

To solve the equation by complete the square for expression.

  $3x^2-18x+12=0$

Answer to Problem 28E

The solutions are $3+\sqrt{5}$ and $3-\sqrt{5}$

Explanation of Solution

Given information:

Expression

  $3x^2-18x+12=0$

Calculation:

Original equation

  $3x^2-18x+12=0$

Divide by 3 both sides

  $\frac{3x^2-18x+12}{3}=\frac{0}{3}$

Simplify

  $x^2-6x+4=0$

Subtract $4$ both sides

  $x^2-6x=-4$

Since ${\left(\frac{6}{2}\right)}^2=9$ , add 9 to both sides

  $x^2-6x+9=-4+9$

Factor $x^2-6x+9$

  ${(x-3)}^2=5$

On solving

  $x-3=\pm \sqrt{5}$

Add $3$ both sides

  $x=3\pm \sqrt{5}$

Separating the equations

  $x=3+\sqrt{5}$ Or $x=3-\sqrt{5}$

The solutions are $3+\sqrt{5}$ and $3-\sqrt{5}$