SOLUTION: Solve by completeting the square: 3x (squared) - 18x + 24 = 18 (not sure how to get it to type the squared

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Question 113450: Solve by completeting the square:

3x (squared) - 18x + 24 = 18 (not sure how to get it to type the squared
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-18x%2B+24+=+18 Start with the given equation


3x%5E2-18x=-6 Subtract 24 from both sides

3%28x%5E2-6x%29=-6 Factor out the leading coefficient 3. This step is important since we want the x%5E2 coefficient to be equal to 1.



Take half of the x coefficient -6 to get -3 (ie -6%2F2=-3)
Now square -3 to get 9 (ie %28-3%29%5E2=9)



3%28x%5E2-6x%2B9%29=-6%2B9%283%29 Add this result (9) to the expression x%5E2-6x inside the parenthesis. Now the expression x%5E2-6x%2B9 is a perfect square trinomial. Now add the result (9)(3) (remember we factored out a 3) to the right side.



3%28x-3%29%5E2=-6%2B9%283%29 Factor x%5E2-6x%2B9 into %28x-3%29%5E2 (note: if you need help with factoring, check out this solver)


3%28x-3%29%5E2=-6%2B27 Multiply 9 and 3 to get 27



3%28x-3%29%5E2=21 Combine like terms on the right side

%28x-3%29%5E2=7 Divide both sides by 3


x-3=0%2B-sqrt%287%29 Take the square root of both sides

x=3%2B-sqrt%287%29 Add 3 to both sides to isolate x.

So the expression breaks down to
x=3%2Bsqrt%287%29 or x=3-sqrt%287%29


So our answer is approximately
x=5.64575131106459 or x=0.354248688935409

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+-+18x+%2B+24+=+18
subtract 24 from both sides
3x%5E2+-+18x+=+-6
divide both sides by 3
x%5E2+-+6x+=+-2
take 1/2 of the coeffecient of x, then square it, then add it to both sides
x%5E2+-+6x+%2B+9+=+-2+%2B+9
%28x+-+3%29%5E2+=+7
x+-+3+=+0+%2B-sqrt%287%29
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x+-+3+=+sqrt%287%29
x+=+3+%2B+sqrt%287%29 answer
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x+-+3+=+-sqrt%287%29
x+=+3+-+sqrt%287%29 answer
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