SOLUTION: Two times the first number subtract 5 is equal to the second number. The sum of the second number and the square of the first number is 115. Find the numbers?

Question 1107014: Two times the first number subtract 5 is equal to the second number. The sum of the second number and the square of the first number is 115. Find the numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two times the first number subtract 5 is equal to the second number.
2a - 5 = b
The sum of the second number and the square of the first number is 115.
a^2 + b = 115
Find the numbers?
In the above equation, replace b with (2a-5) from the 1st equation
a^2 + (2a-5) = 115
a^2 + 2a - 5 - 115 = 0
A quadratic equation
a^2 + 2a - 120 = 0
You can us the quadratic formula but this will factor to
(a+12)(a-10) = 0
Two solutions
a = -12 then b = -29, using the 1st equation to find b
and
a = +10 then b = 15
:
:
You should confirm both these solutions in the 2nd equation
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