SOLUTION: hi i'm in college and i'm so confuse in algebra class. *Solve the quadratic equation by factoring and applying the zero product principle 1)x2 − x − 6 = 0 2)(x &

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: hi i'm in college and i'm so confuse in algebra class. *Solve the quadratic equation by factoring and applying the zero product principle 1)x2 − x − 6 = 0 2)(x &      Log On


   

Question 648510: hi i'm in college and i'm so confuse in algebra class.
*Solve the quadratic equation by factoring and applying the zero product principle
1)x2 − x − 6 = 0
2)(x − 8)2 − 9 = 0
can u please help me? explain to me how to solve the problems?
Answer by Algebraic(50) About Me  (Show Source):
You can put this solution on YOUR website!
Original equations: x%5E2+-+x+-+6+=+0 and %28x-8%292-9+=+0
The zero-product principle states that the factored version of the equation must be set equal to 0 and solved for...
Let's factor and solve the first equation:
Step 1: Factor
x%5E2+-+x+-+6+=+0 can be factored into %28x-3%29%28x%2B2%29+=+0
Step 2: Solve each parenthesis individually
%28x-3%29%28x%2B2%29+=+0
%28x-3%29=0 and %28x%2B2%29+=+0
You want to get 'x' by itself, so add '3' to both sides...
%28x-3%29=0
x=3
You want to get 'x' by itself, so subtract '2' to both sides...
%28x%2B2%29=0
x=-2
So... the roots of the equation x%5E2+-+x+-+6+=+0 are x=3 and x=-2
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Let's solve the other equation:
%28x-8%292-9+=+0
Step 1: Let's rewrite the equation so that the '2' is placed in front of the parenthesis
2%28x-8%29-9+=+0
Step 2: Distribute the '2' to everything in the parenthesis
2%28x-8%29-9+=+0
2x+-+16+-+9+=+0
Step 3: Combine like terms
2x+-+16+-+9+=+0
2x+-+25+=+0
Step 4: Add '25' to both sides in order to get the '2x' by itself
2x+-+25+=+0
2x+=+25
Step 5: Divide both sides by '2' in order to get 'x' by itself
2x+=+25
x+=+%2825%2F2%29
The root of the equation %28x-8%292-9+=+0 is x+=+%2825%2F2%29