Question

2x^2 + x- 6 = 0 by completeing the squares

Answer 1

Answer:

$\implies x =\frac{3}{2}\:Or \:x =-2$

Step-by-step explanation:

2x²+x-6=0

=> 2x²+x=6

/* Divide each term by 2, we get

$x^{2}+\frac{x}{2}=3$

$\implies x^{2}+2\times x\times \frac{1}{4}=3$

$\implies x^{2}+2\times x\times \frac{1}{4}+\left(\frac{1}{4}\right)^{2}=3+\left(\frac{1}{4}\right)^{2}$

$\implies (x+\frac{1}{4})^{2}=3+\frac{1}{16}\\=\frac{48+1}{16}\\=\frac{49}{16}$

$\implies x+\frac{1}{4}=±\frac{7}{4}$

$\implies x=-\frac{1}{4}±\frac{7}{4}$

$\implies x=\frac{-1±7}{4}$

$\implies x =\frac{-1+7}{4}\:Or \:x =\frac{-1-7}{4}$

$\implies x =\frac{6}{4}\:Or \:x =\frac{-8}{4}$

$\implies x =\frac{3}{2}\:Or \:x =-2$

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