Question

dratic equations by factorisation

2x²+x-6=0
6 =​

Answer 1

Use completing the square method.

$2 {x}^{2} + x - 6 = 0 \\ 2x^{2}+x=0 + 6 \\ 2x^{2}+x=6 \\ \frac{2x^{2}+x}{2}=\frac{6}{2} \\ x^{2}+\frac{1}{2}x=\frac{6}{2} \\ x^{2}+\frac{1}{2}x=3 \\ x^{2}+\frac{1}{2}x+\left(\frac{1}{4}\right)^{2}=3+\left(\frac{1}{4}\right)^{2} \\ x^{2}+\frac{1}{2}x+\frac{1}{16}=3+\frac{1}{16} \\ x^{2}+\frac{1}{2}x+\frac{1}{16}=\frac{49}{16} \\ \left(x+\frac{1}{4}\right)^{2}=\frac{49}{16} \\ \sqrt{\left(x+\frac{1}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$

Now, you'll get the values of x as..

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

After simplification...

$\boxed{ \tt \: x=\frac{3}{2}} \\ \boxed{ \tt \: x=-2 }$

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