Question 67541: Solve the following quadratic equation by completing the square:
x^2 – 6x – 3 = 0
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Solve the following quadratic equation by completing the square:
x^2 – 6x – 3 = 0
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Here it is, step-by-step, so after this, you can do it by yourself.
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Add 3 to both sides and you have:
x^2 - 6x = +6
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Write it, leaving a space for the value to make it a perfect square:
x^2 - 6x + __ = + 3
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Determine this value: divide the coefficient of x (which is 6) by 2 and square it. 6/2 = 3, square 3 and you have 9, put 9 in the space. Since you added 9 on the left you have to add 9 on the right to preserve equality.
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x^2 - 6x + 9 = 3 + 9
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(x - 3)^2 = 12; FOIL (x-3)(x-3) to prove it to yourself
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Find the square root of both sides and you have:
x - 3 = +/-SqRt(12)
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x -3 = +/-SqRt(2*2*3) shows we can extract 2*2 from the radical and have:
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x - 3 = +/- 2*SqRt(3)
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Add 3 to both sides, we have two solutions:
x = 3 + 2*SqRt(3)
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x = 3 - 2*SqRt(3)
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Did this make sense to you? Any questions?
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