SOLUTION: Hi all, One more question and I should be about done with algebra for awhile. The directions here say to solve for the roots. p^2+15p+25=6p+5 I have no clue how to do this. Th

Question 12636: Hi all,
One more question and I should be about done with algebra for awhile. The directions here say to solve for the roots.
p^2+15p+25=6p+5
I have no clue how to do this.
Thanks for the help
Answer by AdolphousC(70) (Show Source): You can put this solution on YOUR website!
You need to get Zero on the right side of the equation by subtracting 6p and 5 from both sides of your equation, this leaves you with...

Now you need to find the roots,

Step 1: Multiply the P^2 Coefficient with your constant ( 1 * 20 ) = 20
Step 2: List the factors of 20

20, 1

10, 2

5, 4

-4, -5

-2, -10

-1, -20

Step 3: Out of the factors, are there any that when you add them together give you your P term, in this case 9.

Yes ( 5 + 4 = 9 )
Step 4: Split the middle term into its two factors

<--- Unfoil
Step 5: Group

Step 6: Take out GCF From each group

Step 7: You need two sets of '()' one set is the one term inside '()' the other set is what is left over ( technically factoring out a (P+5) )

Step 8: FOIL to Check
Step 9: the ROOTS of a Quadratic are where the Quadratic crosses the X-Axis, and where the function evaluates to Zero.

In order for to be true either

P + 5 = 0 There for P = -5 OR

P + 4 = 0 There for P = -4
So, -5 and -4 are your roots
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