Question

Question 5 (2 points) (03.06) Solve x2 + 12x + 6 = 0 using the completing-the-square method. (2 points)

Answer 1

The given equation is expressed as

x^2 + 12x + 6 = 0

Subtracting 6 from both sides of the equation, it becomes

x^2 + 12x + 6 - 6 = 0 - 6

x^2 + 12x = - 6

The next step is to add the square of halve the coefficient of x to both sides of the equation.

The coefficient of x is 12

halve of the coefficeint of x is 12/2 = 6

The equation would be

x^2 + 12x + 6^2 = 6^2 - 6

x^2 + 12x + 36 = 36 - 6

Recall that

(x + 6)^2 = (x + 6)(x + 6) = x^2 + 6x + 6x + 36)

Therefore, the equation becomes

(x + 6)^2 = 30

`\begin{gathered} (x+6)^2\text{ = 30} \\ \text{Taking square root of both sides, } \\ \sqrt[]{(x+6)^2\text{ =}}\text{ +- }\sqrt[]{30} \\ x\text{ + 6 = + - 5.477} \\ x\text{ = - 5.477 - 6 or 5.477 - 6} \\ x\text{ = - 11.477 or x = - 0.523} \end{gathered}`

x = - 11.477 or - 0.523