SOLUTION: Identify the solutions to the equation 4x(squared)-20x= -25 by completing the square.

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Question 113940: Identify the solutions to the equation 4x(squared)-20x= -25 by completing the square.
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-20x=-25 Start with the given equation


4%28x%5E2-5x%29=-25 Factor out the leading coefficient 4. This step is important since we want the x%5E2 coefficient to be equal to 1.



Take half of the x coefficient -5 to get -2.5 (ie -5%2F2=-2.5)
Now square -2.5 to get 6.25 (ie %28-2.5%29%5E2=6.25)



4%28x%5E2-5x%2B6.25%29=-25%2B6.25%284%29 Add this result (6.25) to the expression x%5E2-5x inside the parenthesis. Now the expression x%5E2-5x%2B6.25 is a perfect square trinomial. Now add the result (6.25)(4) (remember we factored out a 4) to the right side.



4%28x-2.5%29%5E2=-25%2B6.25%284%29 Factor x%5E2-5x%2B6.25 into %28x-2.5%29%5E2


4%28x-2.5%29%5E2=-25%2B25 Multiply 6.25 and 4 to get 25



4%28x-2.5%29%5E2=0 Combine like terms on the right side

%28x-2.5%29%5E2=0 Divide both sides by 4


x-2.5=0%2B-sqrt%280%29 Take the square root of both sides

x-2.5=0 Take the square root of zero to get zero

x=2.5 Add 2.5 to both sides to isolate x.


So our answer is
x=2.5


Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+4x%5E2-20x%2B25%29+ graph of y=4x%5E2-20x%2B25

Here we can see that the x-intercept is x=2.5, so this verifies our answer.