what two numbers multiplied equal 2 but added equal 5?
xy = 2 x + y = 5
Solve for y; substitute into other equation
y = 2/x x + 2/x = 5
Solve for x
x(x + 2/x) = 5x
x^2 + 2 = 5x
x^2 - 5x + 2 = 0
Complete the square
x^2 - 5x = -2
This is in the form ax^2 + bx. Add (1/2 b)^2 to both sides
x^2 - 5x + (2.5)^2 = -2 + (2.5)^2
x^2 - 5x + (2.5)^2 = 4.25
Take the square root of both sides
x - 2.5 = ±2.061553
x = 2.061553 + 2.5 and x = -2.061553 + 2.5
x = 4.561553 and x = 0.438447
4.561553 * 0.438447 = 1.999999
Rounding errors in the calculation of x accounts for
the slight difference between 2 and our multiplication
4.561553 + 0.438447 = 5