SOLUTION: Problem 1: When twice the second number is subtracted from the first number, the result is -18. The square of the sum of the first number and 2 is equal to the second number minus

Algebra ->  Equations -> SOLUTION: Problem 1: When twice the second number is subtracted from the first number, the result is -18. The square of the sum of the first number and 2 is equal to the second number minus       Log On


   

Question 1100219: Problem 1: When twice the second number is subtracted from the first number, the result is -18. The square of the sum of the first number and 2 is equal to the second number minus 3.
Problem 2: Twice the square of the first number minus the second number is -3. The square of the sum of the first number and 5 is equal to the second number minus 2.
Please include "let statements" and equations. Thank you!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Problem 1:
let a = the first number
let b = the second number
:
Write an equation for each statement
"When twice the second number is subtracted from the first number, the result is -18."
a - 2b = -18
rearrange for substitution in the 2nd equation
-2b = -a - 18
multiply by -1
2b = a + 18
b = %28a%2B18%29%2F2
:
"The square of the sum of the first number and 2 is equal to the second number minus 3."
(a+2)^2 = b - 3
FOIL (a+2)(a+2)
a^2 + 4a + 4 = b - 3
replace b with %28a%2B18%29%2F2
a^2 + 4a + 4 = %28a%2B18%29%2F2 - 3
get rid of the fraction, multiply by 2
2a^2 + 8a + 8 = a + 18 - 6
2a^2 + 8a + 8 = a + 12
2a^2 + 8a - a + 8 - 12 = 0
2a^2 + 7a - 4 = 0
Assuming they are using integers, it must factor
(2a-1)(a+4) = 0
two solutions
a = 1/2
and
a = -4 the integer solution is what we want here
:
find b using the 1st equation when a = -4
-4 - 2b = -18
multiply by -1
4 + 2b = 18
2b = 18 - 4
2b = 14
b = 7
:
1st number is -4, 2nd number is +7
:
:
see if that checks out in the 2nd equation
(-4+2)^2 = 7 - 3
-2^2 = 4
4 = 4
:
:
Problem 2: Much like the first problem
Twice the square of the first number minus the second number is -3.
2a^2 - b = -3
-b = -2a^2 - 3
b = 2a^2 + 3
:
The square of the sum of the first number and 5 is equal to the second number minus 2.
(a+5)^2 = b - 2
FOIL, Replace b with 2a^2 + 3
a^2 + 10a + 25 = 2a^2 + 3 - 2
a^2 + 10a + 25 = 2a^2 + 1
combine on the right
0 = 2a^2 - a^2 - 10a - 25 + 1
0 = a^2 - 10a - 24
(a - 12)(a + 2) = 0
Two solutions
a = 12
and
a = -2
Find b when a = 12
b = 2(12^2) + 3
b = 2(144) + 3
b = 289
See if that works in the 2nd equation
(12 + 5)^2 = 289 - 2
17^2 = 287
:
Why don't you find b when a = -2 and check that out