Question

2x^2+x-4=0 tell in completing squreing​

Answer 1

$\huge\underline\mathfrak\red{Correct\:Question:-}$

Find the roots of the following quadratic equation

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

by the method of completing the square.

$\huge \underline \mathfrak\green{Solution:-}$

Given, quadratic equation

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

$\implies 2 {x}^{2} + x =4$

Dividing by 2 on both sides

${x}^{2} + \frac{x}{2} =2$

${x}^{2} +2\times \frac{x}{2} \times 1=2$

${x}^{2} +2\times 1 \times \frac{x}{2} + \frac {{x}{2}}^2-\frac{{x}{2}}^2=2$

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

${{x}+{\frac{x}{2}}}^{2} =\frac{4-x}{2}$

${x}+{\frac{x}{2}} =\squareroot\frac{4-x}{2}$

${{x}+{\frac{x}{2}}}^{2} =\frac{4-x}{2}$

${{x}+{\frac{x}{2}}}^{2} =\frac{4-x}{2}$