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solve for x

 Sep 16, 2018
 #1
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Solve for x:
x^2 + 4 x + 13 = 0

Solve the quadratic equation by completing the square.
Subtract 13 from both sides:
x^2 + 4 x = -13

Take one half of the coefficient of x and square it, then add it to both sides.
Add 4 to both sides:
x^2 + 4 x + 4 = -9

Factor the left hand side.
Write the left-hand side as a square:
(x + 2)^2 = -9

Eliminate the exponent on the left-hand side.
Take the square root of both sides:
x + 2 = 3 i or x + 2 = -3 i

Look at the first equation: Solve for x.
Subtract 2 from both sides:
x = -2 + 3 i or x + 2 = -3 i

Look at the second equation: Solve for x.
Subtract 2 from both sides:
 
 x = -2 + 3i     or       x = -2 - 3i

 Sep 16, 2018

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