Question

Solve the equation 2x² + x - 4 = 0 , by the method of completing the square .​

Answer 1

Step-by-step explanation:

We have,

$2 {x}^{2} + x - 4 = 0$

$\implies {x}^{2} + \frac{x}{2} - 2 = 0$

$\implies {x}^{2} + 2 \times \frac{1}{4} \times x +( \frac{1}{4} )^{2} - ({ \frac{1}{4} })^{2} - 2 = 0$

$\implies(x + \frac{1}{4} )^{2} - \frac{33}{16} = 0$

$\implies(x + \frac{1}{4} )^{2} - {( \frac{ \sqrt{33} }{4} })^{2} = 0$

$\implies(x + \frac{1}{4} - \frac{ \sqrt{33} }{4} )(x + \frac{1}{4} + \frac{ \sqrt{33} }{4} ) = 0$

$\implies \: x = \frac{1 - \sqrt{33} }{4} \: \: or \: \: x = \frac{1 + \sqrt{33} }{4}$