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) (Show Source): You can put this solution on YOUR website!
Factor out the leading coefficient 3. This step is important since we want the coefficient to be equal to 1.
Take half of the x coefficient -2 to get -1 (ie )
Now square -1 to get 1 (ie )
Add this result (1) to the expression inside the parenthesis
Add 1(3) to the other side (remember we factored out a 3)
Now the left side is a complete square
Factor into (note: if you need help with factoring, check out this solver)
Multiply 1 and 3 to get 3
Combine like terms
Divide both sides by 3
Take the square root of both sides
Add 1 to both sides
So the expression breaks down to
or
So our answer is approximately
or
Here is visual proof
graph of
When we use the root finder feature on a calculator, we would find that the x-intercepts are and , so this verifies our answer.
Answer by mathbird(71) (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
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