SOLUTION: Please help me solve this equation: 5x^2-20x-20=5 It is called completing the square and has to do with solving quadratic equations.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this equation: 5x^2-20x-20=5 It is called completing the square and has to do with solving quadratic equations.      Log On


   

Question 196865This question is from textbook McDougal Littell Algebra 1
: Please help me solve this equation: 5x^2-20x-20=5
It is called completing the square and has to do with solving quadratic equations. This question is from textbook McDougal Littell Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2-20x-20=5 Start with the given equation.


5x%5E2-20x-20-5=0 Subtract 5 from both sides.


5x%5E2-20x-25=0 Combine like terms.


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Now let's complete the square for the left side expression 5x%5E2-20x-25


5x%5E2-20x-25 Start with the given expression.


5%28x%5E2-4x-5%29 Factor out the x%5E2 coefficient 5. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -4 to get -2. In other words, %281%2F2%29%28-4%29=-2.


Now square -2 to get 4. In other words, %28-2%29%5E2=%28-2%29%28-2%29=4


5%28x%5E2-4x%2Bhighlight%284-4%29-5%29 Now add and subtract 4 inside the parenthesis. Make sure to place this after the "x" term. Notice how 4-4=0. So the expression is not changed.


5%28%28x%5E2-4x%2B4%29-4-5%29 Group the first three terms.


5%28%28x-2%29%5E2-4-5%29 Factor x%5E2-4x%2B4 to get %28x-2%29%5E2.


5%28%28x-2%29%5E2-9%29 Combine like terms.


5%28x-2%29%5E2%2B5%28-9%29 Distribute.


5%28x-2%29%5E2-45 Multiply.


So after completing the square, 5x%5E2-20x-25 transforms to 5%28x-2%29%5E2-45. So 5x%5E2-20x-25=5%28x-2%29%5E2-45.


So 5x%5E2-20x-25=0 is equivalent to 5%28x-2%29%5E2-45=0.


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Now let's solve 5%28x-2%29%5E2-45=0


5%28x-2%29%5E2-45=0 Start with the given equation.


5%28x-2%29%5E2=0%2B45Add 45 to both sides.


5%28x-2%29%5E2=45 Combine like terms.


%28x-2%29%5E2=%2845%29%2F%285%29 Divide both sides by 5.


%28x-2%29%5E2=9 Reduce.


x-2=%22%22%2B-sqrt%289%29 Take the square root of both sides.


x-2=sqrt%289%29 or x-2=-sqrt%289%29 Break up the "plus/minus" to form two equations.


x-2=3 or x-2=-3 Take the square root of 9 to get 3.


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


x=5 or x=-1 Combine like terms.


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Answer:


So the solutions are x=5 or x=-1.