Question 818755: Solve by completing the square.. What value should you add to each side of the equation?
x^2+2x=-6
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x^2 + 2x = -6
x^2 + 2x + 6 = 0
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the above quadratic equation is in standard form, with a=1, b=2, and c=6
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to solve the quadratic equation by using the quadratic formula, plug this:
1 2 6
into this: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has complex roots:
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the two complex roots of the quadratic are:
x = -1 + (2.23606798)i
x = -1 - (2.23606798)i
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check this result by completing the square:
x^2 + 2x = -6
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convert to the complete-square form:
a(x + d)^2 + e = 0
where:
d = b/(2a) = 2/2 = 1
e = c - (b^2/(4a)) = 6 - (4/4) = 5
a=1, b=2, c=6
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a(x + d)^2 + e = 0
(x + d)^2 = -e
(x + 1)^2 = -5
x + 1 = sqrt( -5 )
x + 1 = (2.23606798)i
x + 1 - (2.23606798)i = 0
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x + (1 - (2.23606798)i) = 0
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the roots of the above equation are:
x = -1 + (2.23606798)i
x = -1 - (2.23606798)i
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which match the roots obtained from the quadratic formula method above !
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