Question

solve by completing the square:
${2x}^{2} + x - 4 = 0$

Answer 1

2x² + x -4=0
2x² + x = 4 (divide whole eq by 2)
x² + x/2 = 2
x² + x/2 + 1/16  = 2+1/16
(x + 1/4)² = 33/16
√(x+1/4)² = √33/4²
x+1/4 = ±√33/4

hence, $x= \frac{ \sqrt{33} -1}{4}$

$x= \frac{-( \sqrt{33} +1)}{4}$