Question

Solve by completing the square 2x^2+3x-4=0 .

Answer 1

First, divide through by 2 so that we have x² instead of 2x²:

x²+3x/2-2=0.

Now, halve the x coefficient and square it: (3/4)²=9/16. We can write this as:

x²+3x/2+9/16 - (9/16+2)=0; (x+3/4)²=41/16.

Take the square root of each side:

x+3/4=±√41/4, x=-3/4±√41/4=0.85078 and -2.35078 approx.