SOLUTION: Can someone explain how this problem works (if possible step by step so that i can understand it) solve using completing the square, 3x^2-6x=27 the answer is x=1+sqrt(10), 1-sqrt(

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can someone explain how this problem works (if possible step by step so that i can understand it) solve using completing the square, 3x^2-6x=27 the answer is x=1+sqrt(10), 1-sqrt(      Log On


   

Question 198574: Can someone explain how this problem works (if possible step by step so that i can understand it)
solve using completing the square, 3x^2-6x=27 the answer is x=1+sqrt(10), 1-sqrt(10), why?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-6x=27 Start with the given equation.


3x%5E2-6x-27=0 Subtract 27 from both sides.


Now let's complete the square for the left side expression 3x%5E2-6x-27


3x%5E2-6x-27 Start with the given expression.


3%28x%5E2-2x-9%29 Factor out the x%5E2 coefficient 3. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -2 to get -1. In other words, %281%2F2%29%28-2%29=-1.


Now square -1 to get 1. In other words, %28-1%29%5E2=%28-1%29%28-1%29=1


3%28x%5E2-2x%2Bhighlight%281-1%29-9%29 Now add and subtract 1 inside the parenthesis. Make sure to place this after the "x" term. Notice how 1-1=0. So the expression is not changed.


3%28%28x%5E2-2x%2B1%29-1-9%29 Group the first three terms.


3%28%28x-1%29%5E2-1-9%29 Factor x%5E2-2x%2B1 to get %28x-1%29%5E2.


3%28%28x-1%29%5E2-10%29 Combine like terms.


3%28x-1%29%5E2%2B3%28-10%29 Distribute.


3%28x-1%29%5E2-30 Multiply.


So after completing the square, 3x%5E2-6x-27 transforms to 3%28x-1%29%5E2-30. So 3x%5E2-6x-27=3%28x-1%29%5E2-30.


So 3x%5E2-6x-27=0 is equivalent to 3%28x-1%29%5E2-30=0.

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Now let's solve 3%28x-1%29%5E2-30=0


3%28x-1%29%5E2-30=0 Start with the given equation.


3%28x-1%29%5E2=0%2B30Add 30 to both sides.


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


%28x-1%29%5E2=%2830%29%2F%283%29 Divide both sides by 3.


%28x-1%29%5E2=10 Reduce.


x-1=%22%22%2B-sqrt%2810%29 Take the square root of both sides.


x-1=sqrt%2810%29 or x-1=-sqrt%2810%29 Break up the "plus/minus" to form two equations.


x-1=sqrt%2810%29 or x-1=-sqrt%2810%29 Simplify the square root.


x=1%2Bsqrt%2810%29 or x=1-sqrt%2810%29 Add 1 to both sides.


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Answer:


So the solutions are x=1%2Bsqrt%2810%29 or x=1-sqrt%2810%29.



Note: you can use the quadratic formula to verify your answer.