SOLUTION: Solve the equation by completing the square. Round to the nearest hundredth if necessary. 3x^2-6x-24=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the equation by completing the square. Round to the nearest hundredth if necessary. 3x^2-6x-24=0      Log On


   

Question 195673: Solve the equation by completing the square. Round to the nearest hundredth if necessary.
3x^2-6x-24=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-6x-24 Start with the left side of the given equation.


3%28x%5E2-2x-8%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%29-8%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%29-1-8%29 Group the first three terms.


3%28%28x-1%29%5E2-1-8%29 Factor x%5E2-2x%2B1 to get %28x-1%29%5E2.


3%28%28x-1%29%5E2-9%29 Combine like terms.


3%28x-1%29%5E2%2B3%28-9%29 Distribute.


3%28x-1%29%5E2-27 Multiply.


So after completing the square, 3x%5E2-6x-24 transforms to 3%28x-1%29%5E2-27. So 3x%5E2-6x-24=3%28x-1%29%5E2-27.


So 3x%5E2-6x-24=0 is equivalent to 3%28x-1%29%5E2-27=0.


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Now let's solve 3%28x-1%29%5E2-27=0


3%28x-1%29%5E2-27=0 Start with the given equation.


3%28x-1%29%5E2=0%2B27Add 27 to both sides.


3%28x-1%29%5E2=27 Combine like terms.


%28x-1%29%5E2=%2827%29%2F%283%29 Divide both sides by 3.


%28x-1%29%5E2=9 Reduce.


x-1=0%2B-sqrt%289%29 Take the square root of both sides.


x-1=sqrt%289%29 or x-1=-sqrt%289%29 Break up the "plus/minus" to form two equations.


x-1=3 or x-1=-3 Take the square root of 9 to get 3.


x=1%2B3 or x=1-3 Add 1 to both sides.


x=4 or x=-2 Combine like terms.


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Answer:


So the solutions are x=4 or x=-2.