Solve by using the most appropriate method. Give irrational roots in simplest radical form.
1. 5x(x-3)+4(x+4) = 31-7x^2
2. (x+3)^2 +6(x+3)=16
Thank you in advance!!!! :)
2007-05-25 09:10:29 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1.
5x(x-3)+4(x+4) = 31-7x^2
Multiply everything through...
5x^2 - 15x + 4x + 16 = 31 - 7x^2
12x^2 - 11x - 15 = 0
(4x + 3)(3x - 5) = 0
So, x = -3/4 and 5/3
2.
(x+3)^2 +6(x+3)=16
This one is a little unique... You could mulitply everything through and solve like #1, but here's a little different way to do it.
Let M = x + 3, substitute that in the equation:
Now, you have
M^2 + 6M = 16
M^2 + 6M - 16 = 0
(M + 8)(M - 2) = 0
M = -8 and 2
Now, substitute back the M = x + 3.
x + 3 = -8 AND x + 3 = 2
x = -11 AND x = -1
2007-05-25 09:18:36 · answer #1 · answered by Mathematica 7 · 1⤊ 0⤋
NUMBER ONE
5x(x-3)+4(x+4) = 31-7x^2
= 5x^2 - 15x + 4x + 16 = 31 - 7x^2
= 5x^2 + 7x^2 - 15x + 4x + 16 - 31 = 0
= 12x^2 - 11x - 15 = 0
= (4x + 3) (3x - 5) = 0
first factor: (4x+3)
4x + 3 = 0
4x = -3
x = -3/4
second factor: (3x - 5)
3x - 5 = 0
3x = 5
x = 5/3
NUMBER TWO
long method
(x+3)^2 + 6(x+3) = 16
= (x + 3) (x + 3) + 6(x + 3) - 16 = 0
= x^2 + 3x + 3x + 9 + 6x + 18 - 16 = 0
= x^2 + 6x + 9 + 6x + 18 - 16 = 0
= x^2 + 12x + 11 = 0
= (x + 1) (x + 11) = 0
therefore, x = -1, -11
short method
(x+3)^2 + 6(x+3) = 16
= (x + 3)^2 + 6(x + 3) - 16 = 0
= [(x + 3) - 2] [(x + 3) + 8] = 0
first factor: (x + 3) - 2
x + 3 - 2 = 0
x + 1 = 0
x = -1
second factor: (x + 3) + 8
x + 3 + 8 = 0
x + 11 = 0
x = -11
2007-05-25 16:48:15 · answer #2 · answered by Kasparov 2 · 0⤊ 0⤋
1. 5x(x-3)+4(x+4) = 31-7x^2
5x^-15x +4x+16 =31-7x^2
12x^2 -11x -15 = 0
(4x+3)((3x-5) = 0
x = -3/4, 5/3
2. (x+3)^2 +6(x+3)=16
(x+3)[x+3) +6] = 16
= (x+3(x +9 )=16
x^2+12x +11=0
(x+1)(x+11)= 0
x = -1,-11
2007-05-25 18:07:37 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
1. can be reformulated as
12x^2 - 11x - 15 = 0
using quadratic formula roots are
(11 +- 29)/24 = 5/3 and -3/4
2. can be reformulated as
x^2 + 12x + 11 = 0
which can be factored as
(x + 11)(x + 1) = 0
roots are -11 and -1
2007-05-25 16:20:17 · answer #4 · answered by Chet 1 · 0⤊ 0⤋
1: 1 2/3 and -3/4
2:-1 and -11
2007-05-25 18:12:55 · answer #5 · answered by Danny 4 · 0⤊ 0⤋
distribute first
5x^2 -15x+4x+16=31-7x^2
Then combine like terms
2007-05-25 16:17:54 · answer #6 · answered by simply-remember 5 · 0⤊ 0⤋
yo mama
2007-05-25 16:43:22 · answer #7 · answered by evilknieval 2 · 0⤊ 1⤋
what grade are you in just curious i only started it this yr and im in 10th grade
2007-05-25 16:21:29 · answer #8 · answered by Anonymous · 0⤊ 1⤋
do your own damn homework
2007-05-25 16:19:51 · answer #9 · answered by Anonymous · 0⤊ 4⤋