Question

Solve x2 + 12x + 6 = 0 using the completing-the-square method.

A) x = negative six plus or minus the square root of thirty

B) x = six plus or minus the square root of thirty

C) x = negative six plus or minus the square root of six

D) x = six plus or minus the square root of six

Answer 1

Answer:

Option A is correct.

$x = -6 \pm \sqrt{30}$

Explanation:

Given the expression: $x^2+12x+6 = 0$

$x^2+12x+6=0$  

Subtract 6 from both sides, we get

$x^2+12x=-6$  

halve linear coefficient,then  square it, and add it to both sides

$x^2+12x+36=30$

Now, the left side is a perfect square

$(x+6)^2=30$  

Now, take square root to both sides.

$x+6=\sqrt{30}$ 

Subtract 6 from both sides, we get;

$x = -6 \pm \sqrt{30}$

So, the solutions are : $x = -6 \pm \sqrt{30}$

Answer 2

Answer:

The correct answer is A

$x=-6\pm \sqrt{30}$

Step-by-step explanation:

The given expression is

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

Add $-6$ to both sides

$x^2+12x=-6$

Add $(\frac{12}{2} )^2=(6)^2$ to both sides.

$x^2+12x+(6)^2=-6+(6)^2$

We got a perfect square on the left hand side

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

Simplify the left hand side to get,

$(x+6)^2=30$

Take square root of both sides

$(x+6)=\pm \sqrt{30}$

Solve for $x$.

$x=-6\pm \sqrt{30}$