Question

Solve $x ^ { 2 } +7x+12=0$ by completing the square.

Answer 1

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

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

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

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

• 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

x^2 + 7x + 12 = 0
x^2 + 4x + 3x + 12 = 0
x(x + 4) + 3(x + 4) = 0

(x + 4) (x + 3)
Now Here X can be (-3) Or (-4)

Check:

X As (-4)
(-4)^2 + 7(-4) + 12 = 0
16 - 28 + 12
28 - 28 = 0

X As (-3)
(-3)^2 + 7(-3) + 12 = 0
9 - 21 + 12 = 0
21 - 21 = 0

Hope it helps you