How do you solve this quadratic equation for completing the square?: 4x^2 + 12x -7=0

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steveschoen | College Teacher | (Level 1) Associate Educator

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Hi, Rosey,

There can be a couple of ways to do this.  Myself, I like to add 7 to both sides first.  That gives us:

4x^2 + 12x = 7

Then, I divide each side by 4.  That gives us:

x^2 + 3x = 7/4

Because, dividing the left side by 4, you have to divide 4x^2 and 12x by 4, both of them.

Then, you take half of 3 and square that result.  Half of 3 is 1.5.  Squaring that, we have 2.25.  We add that to each side.  Thus:

x^2 + 3x + 2.25 = 4

That 2.25 allows the left side to be factored into (x+1.5)^2

(x+1.5)^2 = 4

Taking the square root of each side:

x+1.5 = +-2

subtracting 1.5 from each side:

x = -1.5 +- 2 = -3.5, 0.5

So, x = -3.5 and x = 0.5

Good Luck, Rosey.  I hope you understand the method.

Till Then,

Steve

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