How do you solve 4x^2 +12x=29 by completing the square?

1 Answer
Douglas K.
Jan 25, 2017

Please see the explanation.

Explanation:

Divide both sides by 4:

x^2 + 3x = 29/4

Add a^2 to both sides:

x^2 + 3x + a^2= 29/4 + a^2" [1]"

Using the pattern (x+a)^2 = x^2 + 2ax + a^2, set the middle term of the pattern equal to the middle term on the left of equation [1]:

2ax = 3x

Divide both sides of the equation 2x:

a = 3/2

Substitute 3/2 for "a" on both sides of equation [1]:

x^2 + 3x + (3/2)^2= 29/4 + (3/2)^2" [2]"

We know that the left side of equation [2] is a perfect square, therefore, we can substitute the left side of the pattern with a = 3/2 into equation [2]:

(x + 3/2)^2= 29/4 + (3/2)^2" [3]"

Simplify the right side of equation [3]:

(x + 3/2)^2= 38/4" [4]"

Use the square root on both sides:

x + 3/2= +-sqrt38/2" [5]"

Subtract 3/2 form both sides:

x = -3/2 +-sqrt38/2" [6]"

Split equation [6] into two equations:

x = -(3 +sqrt38)/2 and x = -(3 -sqrt38)/2

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