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Question 529966: Please help me with this. I have tried on my own...but, not getting it.
I have to solve x^2 + 6x = 16 by Completing the square.
1.I have to show what is added to each side to complete the square (using boxes)
2. I have to evaluate the square roots and
3.simplify any radicals with plus,minus sign
4. I have to solve the resulting equation and indicate solutions.
Thank you for your help with any part of this!
Found 2 solutions by bucky, ptaylor:
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given to solve by completing the square:
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x^2 + 6x = 16
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First of all, make sure that the coefficient (multiplier of the x^2 term is 1. If it isn't then you need to divide the entire equation (all terms on both sides) by the multiplier of the x^2 term. (For example: if the x^2 term were 3x^2 you would divide all terms on the left and right sides by 3 to make it just x^2.) In this problem the multiplier of the x^2 term is 1 (which you don't normally show) so you don't have to worry about about this step.
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Next you have to get the constant term on the right side of the equation. In the problem you were given, the constant term is already on the right-hand side by itself, so you don't have to worry about doing this step.
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Now, look at the multiplier of the x term. It is 6. Whatever it may be in other problems, divide it by 2, square the result, and add it to both sides of the equation. For this problem, divide the +6 by 2 to get +3. Then square the +3 to get +9. This is the amount that you add to both sides of the equation as follows:
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x^2 + 6x + 9 = 16 + 9
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Put the boxes around the +9 on both sides of this equation. You have now made the left side of this equation a perfect square. It can be factored into the form (x + b)^2 where be is the answer you got by dividing the multiplier of the x term by 2. In this problem that answer was +3. So the equation can be written as:
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(x + 3)^2 = 16 + 9
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Simplify by adding the two constants on the right side to get:
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(x + 3)^2 = 25
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Now take the square root of both sides and you have:
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(x + 3) = +- 5
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Finally, get rid of the +3 on the left side by subtracting 3 from both sides and you get:
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x = -3 +-5
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The two answers to this problem result from - 3 + 5 and - 3 - 5. The answers, therefore are x = +2 and x = -8. You can check these answers by substituting each of them, one at a time, into x^2 + 6x to ensure that they do make the x^2 + 6x on the left side equal to the +16 on the right side. (You will find that they are correct.)
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I tried to write the answer so that it is general. If you follow the above steps as described, you will be able to solve any quadratic equation by completing the square.
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Hope this helps you to understand the process in "recipe" form.
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Answer by ptaylor(2198)  (Show Source):
You can put this solution on YOUR website! OK
x^2+6x=16
Let's add 9 to each side (half of the x coefficient squared)
x^2+6x+9=16+9
(x+3)^2=25 take sqrt of each side
x+3=+-5
x=-3+-5
x=-8 and
x=2
This may be a useful tutorial for you
Take the general form of the quadratic:
Ax^2+Bx+C=0
(1) Subtract C from each side
Ax^2+Bx=-C
(2) Divide each term by A
x^2+(B/A)x=-C/A
(3) Take half of the x coefficient, square it and add it to each side
Half of B/A=B/2A and when we square it, we have B^2/4A^2. Now we add it to each side:
x^2+(B/A)x+B^2/4A^2=(-C/A)+B^2/4A^2
Now the left side is a perfect square:
(x+B/2A)^2=(B^2-4AC)/4A2
(4) Take the sqrt of both sides:
(x+B/2A)=+-SQRT(B^2-4AC)/2A or
x=(-B+-SQRT(B^2-4AC))/2A
Hope this helps---ptaylor
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