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) (Show Source): You can put this solution on YOUR website!
Factoring
Notice that 
and  = -10)
, so:
(x - 13) = 0)
Now use the Zero Product Rule ( 
if and only if 
or 
)
So:
(x - 13) = 0)
means:
= 0 \ \ \Rightarrow\ \ x = -3)
or
= 0 \ \ \Rightarrow\ \ x = 13)
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:
^2 = 64)
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:
 \pm sqrt{(-10)^2 - 4(1)(-39)}}{2(1)} )
I sincerely hope that you were not surprised that all three methods produced the same result.
John
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