2 x square x 4 is equal to zero

Asked by admin @ in Math viewed by 334 People

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

Answered by admin @


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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