SOLUTION: Find two numbers (exactly) whose product is 15 and whose sum is 10.

Question 667557: Find two numbers (exactly) whose product is 15 and whose sum is 10.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find two numbers (exactly) whose product is 15 and whose sum is 10.
:
Two equations
x*y = 15
and
x + y = 10
y = (10-x)
replace y in the 1st equation
x(10-x) = 15
10x - x^2 = 15
Arrange as a quadratic equation on the right
0 = x^2 - 10x + 15
use the "complete the square" method here
x^2 - 10x + ___ = -15
Find the value that completes the square (10/2)^2 = 25; add to both sides
x^2 - 10x + 25 = -15 + 25
(x-5)^2 = 10
Find the square root of both sides
x - 5 = +/-
Two solutions
x = 5 +
and
x = 5 -
:
:
Find these values on a calc, confirm that, when multiplied, they = 15
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