Question

How do you complete the square to solve `2x^2 + 6x =5`?

Answer 1

`2x^2+6x = 5`

Extract the common constant factor on the left side
`2(x^2+3x) = 5`

Complete the square
`2(x^2+3x+(3/2)^2) = 5 + 9/2`

Re-write as a square equal to a constant
`(x+3/2)^2 = 19/4`

Take the square root of both sides
`x+3/2 = +-sqrt(19)/2`

Isolate `x` for the final solution
`x = (-3+-sqrt(19))/2`