Question

2xsquare +x-4=0 by completing square method ​

Answer 1

Step-by-step explanation:

NSWER

The given quadratic equation is

2x

2

+x−4=0

⇒x

2

+

2

x

−2=0

⇒x

2

+

2

x

=2

On adding both sides

16

1

we get

x

2

+

2

x

+

16

1

=2+

16

1

⇒(x+

4

1

)

2

=

16

33

⇒x+

4

1

=±

4

33

⇒x=±

4

33

−

4

1

⇒x=

4

−1−

33

,

4

−1+

33

Answer 2

$\large\underline\mathfrak{Given:-}$

• $\mathbb{equation:-} \: \: {2x}^{2} \: + \: x \: - \: 4 \: \: = \: \: 0$

$\large\underline\mathfrak{To \: \: find:-}$

• $\mathbb{ find \: \: the \: \: value \: \: of \: \: x \: \: by \: \: completing \: \: the \: \: square \: \: method.}$

$\huge\underline\mathfrak{Solutions:-}$

• $\mathbb{equation:-} \: \: {2x}^{2} \: + \: x \: - \: 4 \: \: = \: \: 0$

$\leadsto \: {2x}^{2} \: + \: x \: - \: 4 \: \: = \: \: 0$

$\leadsto \: \frac{{2x}^{2}}{2} \: + \: \frac{x}{2} \: - \: \frac{4}{2} \: \: = \: \: \frac{0}{2}$

$\leadsto \: {x}^{2} \: + \: \frac{x}{2} \: - \: {2} \: \: = \: \: {0}$

$\underline\mathbb{write \: \: the \: \: equation \: \: in \: \: the \: \: form:-}$

$\: \: \: \: \: \: \large\fbox{{{x}^{2} \: + \: {bx} \: \: = \: \: {c}}}$

$\: \: \: \: \: \leadsto \: {x}^{2} \: + \: \frac{x}{2} \: \: = \: \: {2}$

$\underline\mathbb{Add \: \: {{(\frac{1}{2})}^{2}} \: \: on \: \: both \: \: sides.}$

$\: \: \: \: \: \leadsto \: {x}^{2} \: + \: \frac{x}{2} \: + \: \frac{1}{16} \: \: = \: \: {2} \: + \: \frac{1}{16}$

$\: \: \: \: \: \leadsto \: {({x} \: + \: \frac{1}{4})}^{2} \: \: = \: \: {2} \: + \: \frac{1}{16}$

$\: \: \: \: \: \leadsto \: {({x} \: + \: \frac{1}{4})}^{2} \: \: = \: \: \frac{33}{16}$

$\: \: \: \: \: \leadsto \: {x} \: + \: \frac{1}{4} \: \: = \: \: \sqrt{\frac{33}{16}}$

$\: \: \: \: \: \leadsto \: {x} \: + \: \frac{1}{4} \: \: = \: \: {\frac{\sqrt33}{16}}$

$\: \: \: \: \: \leadsto \: {x} \: = \: \: {\frac{\pm\sqrt{33}}{16}} \: - \: \frac{1}{4}$

$\: \: \: \: \: \leadsto \: {x} \: = \: \: {\frac{\sqrt{33} \: - \: 1}{4}} \: \: \: Or \: \: \: {x} \: = \: \: {\frac{{ \: - \: (\sqrt{33} \: + \: 1)}}{4}}$

$\underline\mathbb{So,}$

$\: \: \: \: \: the \: \: roots \: \: of \: \: the \: \: given \: \: equation \: \: are:-$

$\: \: \: \: \: \: \large\fbox{ {x} \: = \: \: {\frac{\sqrt{33} \: - \: 1}{4}} \: \: \: Or \: \: \: {x} \: = \: \: {\frac{{ \: - \: (\sqrt{33} \: + \: 1)}}{4}}}$

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