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

Question 113940: Identify the solutions to the equation 4x(squared)-20x= -25 by completing the square.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Factor out the leading coefficient 4. This step is important since we want the coefficient to be equal to 1.

Take half of the x coefficient -5 to get -2.5 (ie )
Now square -2.5 to get 6.25 (ie )

Add this result (6.25) to the expression inside the parenthesis. Now the expression is a perfect square trinomial. Now add the result (6.25)(4) (remember we factored out a 4) to the right side.

Factor into

Multiply 6.25 and 4 to get 25

Combine like terms on the right side

Divide both sides by 4

Take the square root of both sides

Take the square root of zero to get zero

Add 2.5 to both sides to isolate x.

So our answer is

Here is visual proof

graph of

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

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