Chapter 7, Problem 2CT

To determine

To find: the value of $x$ by completing the square.

Answer to Problem 2CT

The value of $x$ is $\frac{\sqrt{3}-3}{2},\frac{-\sqrt{3}-3}{2}$ .

Explanation of Solution

Given information:

The equation is $2x^2+6x+3=0$ .

Calculation: to complete the square, first subtract $3$ from both side and then divide by $2$ , and then add ${\left(\frac{3}{2}\right)}^2$ both side, and then simplify for value of $x$ ,

$\begin{array}{l}2x^2+6x+3=0\\ 2x^2+6x=-3\text{ [subtract 3 from both side]}\\ x^2+3x=-\frac{3}{2}\text{ [divide by 2]}\\ x^2+3x+{\left(\frac{3}{2}\right)}^2=-\frac{3}{2}+{\left(\frac{3}{2}\right)}^2\text{ [add }{\left(\frac{3}{2}\right)}^2\text{ both side]}\\ {\left(x+\frac{3}{2}\right)}^2=\frac{3}{4}\text{ [simplify]}\\ x+\frac{3}{2}=\pm \frac{\sqrt{3}}{2}\text{ [square root]}\\ x=\frac{\sqrt{3}-3}{2},\frac{-\sqrt{3}-3}{2}\text{ [simplify]}\end{array}$

Thus, The value of $x$ is $\frac{\sqrt{3}-3}{2},\frac{-\sqrt{3}-3}{2}$ .