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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Solve x2 + 12x + 6 = 0 using the completing-the-square method.
Solution:
Given x2 + 12x + 6 = 0
The technique of completing the square means, we need to add a term which makes the equation a perfect square
The given equation resembles a quadratic equation, where a = 1, b = 12 and c = 6
The term that needs to be added is (-b/2)2
(-12/2)2 = (-6)2 = 36
x2 + 12x + 6 + 36 = 0 + 36
x2 + 12x + 36 = 36 - 6 = 30
x2 + 2(x)(6) + 62 = (√30)2
This resembles a2 + 2ab + b2 = (a + b)2
(x + 6)2 = (√30)2
Applying square-root on both sides, we get
x + 6 =±√30
x = +√30 - 6 or -√30 - 6
Therefore, the solution for x2 + 12x + 6 = 0 is x = +√30 - 6 or -√30 - 6
Solve x2 + 12x + 6 = 0 using the completing-the-square method.
Summary:
By solving x2 + 12x + 6 = 0 using the completing-the-square method, we got a solution as x = √30 - 6 or -√30 - 6.
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