Question

2x² + 2x = 24, compeleting the square. ​

Answer 1

$\underline{\pink{ Completing \: Square \:method : }}$

$Given \: Quadratic \: equation :$

$2x^{2} + 2x = 24$

/* Dividing each term by 2 , we get */

$\implies x^{2} + x = 12$

$\implies x^{2} + 2 \times x\times \frac{1}{2} = 12$

$\implies x^{2} + 2 \times x\times \frac{1}{2} + \Big(\frac{1}{2}\Big)^{2} = 12 + \Big(\frac{1}{2}\Big)^{2}$

$\implies \Big( x + \frac{1}{2}\Big)^{2} = 12 + \frac{1}{4}$

$\implies \Big( x + \frac{1}{2}\Big)^{2} = \frac{48+1}{4}$

$\implies \Big( x + \frac{1}{2}\Big)^{2} = \frac{49}{4}$

$\implies x + \frac{1}{2}= \pm \sqrt{\frac{49}{4}}$

$\implies x = - \frac{1}{2} \pm \frac{7}{2}$

$\implies x = - \frac{1}{2} + \frac{7}{2} \: Or \: - \frac{1}{2} + \frac{7}{2}$

$\implies x = \frac{-1+7}{2} \: Or \: \frac{-1 -7}{2}$

$\implies x = \frac{6}{2} \: Or \: \frac{-8}{2}$

$\implies x = 3 \: Or \: x = -4$

Therefore.

$\green { x = 3 \: Or \: x = -4}$

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