SOLUTION: i need help with these problem i have been doing them for days and they are giving me a headache i hope that this isn't to much to ask for. I am problem by factoring. 1. 3a^2+a=

Question 537392: i need help with these problem i have been doing them for days and they are giving me a headache i hope that this isn't to much to ask for. I am problem by factoring.
1. 3a^2+a=a^2+10a+11
2.n(n+3)=70
3.b(5b-4)=12
4.4t^2-9+16=15-4t^2
5.(2k+4)(2k+9)=3^2+11k
6.5+6y(y+2)=5y+8
7.(m-3)^2=64
I know these are a lot of problem but i really tried to solving them and now I'm just giving up. I understand if you don't answer them all and again thank you every much.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. 3a^2 + a = a^2 + 10a + 11
Combine like terms on the left
3a^2 - a^2 + a - 10a - 11 = 0
2a^2 - 9a - 11 = 0
Factors to
(2a - 11)(a + 1)
two solutions
2a = 11
a = 5.5
and
a = -1
:
2.n(n+3) = 70
n^2 + 3n - 70 = 0
Factors to
(n+10)(n-7) = 0
n = -10
and
n = 7
:
3. b(5b-4) = 12
5b^2 - 4b - 12 = 0
Factors to
(5b + 6)(b - 2) = 0
5b = -6
b = -6/5
b = -1.2
and
b = 2
:
4. 4t^2 - 9 + 16 = 15 - 4t^2; this one look like it has a typo
:
5.(2k+4)(2k+9) = 3^2 + 11k
FOIL the left side
4k^2 + 18k + 8k + 36 = 9 + 11k
4k^2 + 26k - 11k + 36 - 9 = 0
4k^2 + 15k + 25 = 0
no real solutions, a neg discriminant (15^2 - 4*4*25 = -175)
:
6. 5 + 6y(y+2)= 5y + 8
5 + 6y^2 + 12y = 5y + 8
6y^2 + 12y - 5y + 5 - 8 = 0
6y^2 + 7y - 3 = 0
Factors to
(3y-1)(2y+3) = 0
Two solutions
3y = 1
y = 1/3
and
2y = -3
y = -1.5
:
7.(m-3)^2 = 64
(m-3)(m-3) = 64
FOIL
m^2 - 6m + 9 - 64 = 0
m^2 - 6m - 55 = 0
Factors to
(m-11)(m+5) = 0
m = 11
and
m = -5
:
You would be wise to check every one of these solutions in their original equations
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