Question

solve X square + 7 x + 12 = 0 by completing the square​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=-4\:and\:3}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {x}^{2} + 7x + 12 = 0 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Value \: of \: x =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {x}^{2} + 7x + 12 = 0 \\ \\ \tt \:Both \: side \: adding \: ( \frac{b}{2a} )^{2} = (\frac{7}{2 \times 1} )^{2} = \frac{49}{4} \\ \\ \tt: \implies {x}^{2} + 7x + \frac{49}{4} + 12 = \frac{49}{4} \\ \\ \tt: \implies {(x + \frac{7}{2}) }^{2} + 12 = \frac{49}{4} \\ \\ \tt: \implies {(x + \frac{7}{2}) }^{2} = \frac{49}{4} - 12 \\ \\ \tt: \implies {(x + \frac{7}{2}) }^{2} = \frac{49 - 48}{4} \\ \\ \tt: \implies {(x + \frac{7}{2}) }^{2} = \frac{1}{4} \\ \\ \tt: \implies x + \frac{7}{2} = \sqrt{ \frac{1}{4} } \\ \\ \tt: \implies x + \frac{7}{2} = \pm\frac{1}{2} \\ \\ \tt: \implies x = \pm \frac{1}{2} - \frac{7}{2} \\ \\ \tt: \implies x = \frac{ - 7 \pm 1}{2} \\ \\ \green{\tt: \implies x = - 4 \: and \: 3}$

Answer 2

Aɴꜱᴡᴇʀ

☞ The value of X is -4 or 3

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Gɪᴠᴇɴ

➳ x² + 7x +12 = 0

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Tᴏ ꜰɪɴᴅ

➤ Value of x ?

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Sᴛᴇᴘꜱ

❍ Its given that we have to use only completing square method, so,

In this method we have got to add another variable y so to do that,

$\large \sf{}add \: \: { \sf ( \dfrac{ b }{2a}} {)}^{2} \: \: on \: both \: sides$

We get,

$\leadsto{} \sf{} {x}^{2} + 7x + 12 + \frac{49}{4} = \frac{49}{4} \\ \\ \leadsto \sf{} (x + \frac{7}{2} {)}^{2} +12 = \frac{49}{4} \\ \\ \leadsto{} \sf(x + \frac{7}{2} {)}^{2} = \frac{49 - 48}{4} \\ \\ \leadsto{} \sf{}(x + \frac{7}{2} {)}^{2} = \frac{1}{4} \\ \\ \leadsto \sf(x + \frac{7}{2}) = \sqrt{ \frac{1}{4} } \\ \\ \leadsto \sf \red{( x + \frac{7}{2}) =± \frac{1}{2}} \\ \\ \leadsto \sf{}x = \frac{ - 7±1}{2} \\ \\ \pink{ \leadsto\sf{}x = - 4 \: and \: 3}$

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