Solve the equation by completing the square. 0=4x^2-72x

Step-by-step explanation:

First we need to make sure that the leading coefficient is a 1.  Ours is a 4, so we need to factor it out, leaving us with

To complete the square, take half the linear term, square it, then add it to both sides.  But don't forget about that 4 hanging around out front, refusing to be ignored.  Our linear term is 18.  Half of 18 is 9, and 9 squared is 81.  Add 81 into the parenthesis, but what we REALLY added in was 4*81 which is 324:

To solve this, we need to get the x terms all by themselves.  So let's divide both sides by 4 to get

The process of completing the square created a perfect square binomial on the left.  We will state this binomial now:

We isolate the x term by taking the square root of both sides:

x - 9 = ±9

From that we have 2 equations:

x - 9 = 9 and x - 9 = -9

Which means that x = 18 or x = 0

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step-by-step explanation: