SOLUTION: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "x2 - 10x - 39 = 0". I am new to algebra and I have a learning dis

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Question 199094: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "x2 - 10x - 39 = 0".
I am new to algebra and I have a learning dissablitlty could you help.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Factoring

Notice that and , so:



Now use the Zero Product Rule ( if and only if or )

So:

means:



or



Complete the Square



Add the inverse of the constant term to both sides:



Divide the coefficient on the term by 2, square the result, and add that result to both sides (-10 divided by 2 is -5, -5 squared is 25):



The left-hand side is now a perfect square trinomial, so factor it:



Take the square root of both sides, considering both the positive and negative roots:



Add the inverse of the constant term on the left to both sides:



So



or



Quadratic Formula

The equation



is in the form



Where , , and

So:













I sincerely hope that you were not surprised that all three methods produced the same result.

John