Question

find the roots of the equation 2 X square + X - 4 is equal to zero by the method of completing the square

Answer 1

Answer:

$x=\frac{-1±\sqrt{33}}{4}$

Step-by-step explanation:

$Given\: quadratic\: equation\\2x^{2}+x-4=0$

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

/* Divide each term by 2, we get

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

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

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

$\implies \left(x+\frac{1}{4}\right)^{2}=2+\frac{1}{16}\\=\frac{32+1}{16}\\=\frac{33}{16}$

$\implies \left(x+\frac{1}{4}\right)= ±\frac{\sqrt{33}}{4}$

$\implies x = -\frac{1}{4}±\frac{\sqrt{33}}{4}$

$\implies x = \frac{-1±\sqrt{33}}{4}$

Therefore,

$x=\frac{-1±\sqrt{33}}{4}$

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Answer 2

Answer:

REFER THE ATTACHMENT

Hope this helps you