solve by complex ting the square 2x^2+3x-4=0
In questions like this, you should note that the coefficient of thr x^2 term should be a square number also. So multilpy the whole expression by 2. This gives us,
4x^2 + 6x - 8 = 0
We are looking for an expression of the form: ax^2 + 2abx + b^2, which equals (ax + b)^2
we've got the a = 4, so now we need 2abx = 6x.
This gives b = 3/2, Hence b^2 = 9/4.
rearranging, we get
4x^2 + 6x - 8 = 0
4x^2 + 2*(3/2)*x + 9/14 - 9/4 - 8 = 0
(2x + 3/2)^2 - 9/4 - 32/4 = 0
(2x + 3/2)^2 = 41/4
2x + 3/2 = ±√(41)/2
x + 3/4 = ±√(41)/4
x = (-3 ± √(41)) / 4