9514 1404 393
Answer:
x = {-4.4, +2.9}
Step-by-step explanation:
We assume you want to solve ...
2x^2 +3x -41 = -15
Adding 41 and factoring out the leading coefficient gives ...
2(x^2 +3/2x) = 26
Dividing by 2 makes it ...
x^2 +3/2x = 13
We can add the square of half the x-coefficient to "complete the square."
x^2 +3/2x +(3/4)^2 = 13 +(3/4)^2
(x +3/4)^2 = 13.5625 . . . . write the left side as a square
x +3/4 = ±√13.5625 . . . . . take the square root
x = -0.75 ±3.683 = {-4.433, +2.933} . . . . subtract 3/4 and evaluate
The solutions are approximately x = -4.4 and x = 2.9.
