Question

solve for x. write the smaller solution first, and the largest solution second 2x^2-24x+54=0​

Answer 1

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

$\green{\tt{\therefore{Smaller\:x=3}}}$

$\green{\tt{\therefore{Larger\:x=9}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies {2x}^{2} - 24x + 54 = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies smaller \: x = \\ \\ \tt: \implies larger \: x =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {2x}^{2} - 24x + 54 = 0 \\ \\ \tt: \implies {2x}^{2} - 18x - 6x + 54 = 0 \\ \\ \tt: \implies 2x(x - 9) - 6(x - 9) = 0 \\ \\ \tt: \implies (2x - 6)(x - 9) = 0 \\ \\ \tt: \implies 2x - 6 = 0 \\ \\ \tt: \implies 2x = 6 \\ \\ \green{\tt: \implies x = 3} \\ \\ \tt: \implies x - 9 = 0 \\ \\ \green{\tt: \implies x = 9} \\ \\ \green{\tt \therefore Smaller \: value = 3} \\ \\ \green{\tt \therefore Larger \: value = 9}$

Answer 2

Aɴꜱᴡᴇʀ

☞ Smaller x = 3

☞ Larger x = 9

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Gɪᴠᴇɴ

$\sf{w} \tt{e \: have \: the \: equation} \: \: \red{ 2 {x}^{2} - 24x + 54 = 0}$

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ᴛᴏ ꜰɪɴᴅ

➤ The smaller x and the larger x

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Sᴛᴇᴘꜱ

✪ First to find these values of X we first have to factories it.

So,

$\large \dashrightarrow \tt2 {x}^{2} - 24x + 54 = 0\\ \\ \large\tt\dashrightarrow2 {x}^{2} - 18x - 6x + 54 = 0 \\ \\ \large\tt \dashrightarrow{2x(x - 9)} - 6(x - 9) = 0 \\ \\ \large\tt \dashrightarrow \orange{(2x - 6)(x - 9) = 0}$

So now lets equate each one separately with zero,

$\large\tt \leadsto2x - 6 = 0 \\ \\ \large\tt \leadsto x = \cancel \frac{ 6}{2} \\ \\ \tt \large \pink{\leadsto{}x =3 }$

Now the other one,

$\large \tt \longrightarrow{}x - 9 = 0 \\ \\ \large\tt \pink{\longrightarrow{}x = 9}$

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