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

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 342 People

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

Answered by maham237 @ 25/12/2020

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

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