Chapter 9.4, Problem 26PPS

To determine

Solve the equation by completing the square method.

Answer to Problem 26PPS

The solutions are: $-2-3\sqrt{2}i\text{and}-2+3\sqrt{2}i$

Explanation of Solution

Given:

The equation: $3x^2+12x+81=15$

Concept Used:

The perfect square term: ${(x\pm \frac{b}{2})}^2=x^2\pm 2·x·\frac{b}{2}+{(\frac{b}{2})}^2$

Calculation:

The perfect square term: ${(x\pm \frac{b}{2})}^2=x^2\pm 2·x·\frac{b}{2}+{(\frac{b}{2})}^2$

The equation: $3x^2+12x+81=15$

The solutions are: $-2-3\sqrt{2}i\text{and}-2+3\sqrt{2}i$

Thus, the solutions are: $-2-3\sqrt{2}i\text{and}-2+3\sqrt{2}i$