SOLUTION: please help me solve this quadratic equation, Solve using completing the square, 3x^2 - 6x = 27

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Question 92078This question is from textbook Algebra and Trigonometry
: please help me solve this quadratic equation, Solve using completing the square, 3x^2 - 6x = 27
This question is from textbook Algebra and Trigonometry

Found 2 solutions by jim_thompson5910, mathbird:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%28x%5E2-2x%29=27 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 -2 to get -1 (ie -2%2F2=-1)
Now square -1 to get 1 (ie %28-1%29%5E2=1)



3%28x%5E2-2x%2B1%29=27 Add this result (1) to the expression x%5E2-2x inside the parenthesis

3%28x%5E2-2x%2B1%29=27%2B1%283%29 Add 1(3) to the other side (remember we factored out a 3)

Now the left side is a complete square

3%28x-1%29%5E2=27%2B1%283%29 Factor x%5E2-2x%2B1 into %28x-1%29%5E2 (note: if you need help with factoring, check out this solver)



3%28x-1%29%5E2=27%2B3 Multiply 1 and 3 to get 3

3%28x-1%29%5E2=30 Combine like terms

%28x-1%29%5E2=10 Divide both sides by 3


x-1=0%2B-sqrt%2810%29 Take the square root of both sides

x=1%2B-sqrt%2810%29 Add 1 to both sides

So the expression breaks down to
x=1%2Bsqrt%2810%29 or x=1-sqrt%2810%29


So our answer is approximately
x=4.16227766016838 or x=-2.16227766016838

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3x%5E2-6x-27%29+ graph of y=3x%5E2-6x-27


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=4.16227766016838 and x=-2.16227766016838, so this verifies our answer.

Answer by mathbird(71) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2 - 6x = 27
3x^2-6x-27=0
Divide by 3
x^2-2x-9=0
〖(x)〗^2-2(x)(1)+〖(1)〗^2-〖(1)〗^2-9=0
〖(x-1)〗^2-10=0
(x-1)^2=10
x-1=√10
x-1+1=±√10+1
X=±3.16+1
X=4.16: x=-2.16