Question

solve the following equation and find the value of x

(x-3)(2x-5)= 2x^2​

Answer 1

Answer:

The value of x = 15/11

Step-by-step explanation:

(x- 3)(2x-5) = 2x^2

= 2x(x-3)-5(x+3) = 2x^2

= 2x^2-6x-5x+15 = 2x^2

= -11x = -15

= x. = 15/11

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Answer 2

$\huge {\bf{ {Answer : - }}}$

$: \implies \tt(x - 3)(2x - 5) = 2 {x}^{2} \\ \\ \red\bigstar \sf \: \: By \: distributive \: property,$

$\tt: \implies \: 2 {x}^{2} - 5x - 6x + 15 = 2 {x}^{2} \\ \\ \tt : \implies2 {x}^{2} - 11x + 15 = 2 {x}^{2} \\ \\ \tt: \implies 2 {x}^{2} - 11x + 15 - 2 {x}^{2} = 0 \\ \\ \tt: \implies \: - 11x + 15 = 0 \\ \\ \tt : \implies \: - 11x = - 15 \\ \\ \tt : \implies \cancel{- } \: 11x = \cancel{ - } \: 15 \\ \\ : \implies \blue \bigstar \: \underline{\boxed{ \tt{ x = \dfrac{15}{11} }}} \:$

$\huge {\bf {{verification : - }}}$

$\red \bigstar \sf \: By \: substituting \: the \: x \: value \: in \: the \: equation , \:$

$\tt : \implies \bigg( \dfrac{15}{11} - 3 \bigg) \bigg(2 \bigg[ \dfrac{15}{11} \bigg] - 5 \bigg) = 2 \bigg({ \dfrac{15}{11} \bigg) }^{2} \\ \\ \tt : \implies \bigg( \frac{15 - 33}{11} \bigg) \bigg( \frac{30}{11} - 5 \bigg) = 2 \bigg( \frac{225}{121} \bigg) \\ \\ \tt : \implies \bigg( - \frac{18}{11} \bigg) \bigg( \frac{30 - 55}{11} \bigg ) = \bigg( \frac{ 2 \times225 }{121} \bigg) \\ \\ \tt : \implies \bigg( - \frac{18}{11} \bigg) \bigg( - \frac{25}{11} \bigg) = \bigg( \frac{450}{121} \bigg) \\ \\ \tt : \implies \bigg( \frac{ (- 18) (- 25)}{(11)(11)} \bigg) = \bigg(\frac{450}{121} \bigg) \\ \\ \tt : \implies \bigg( \frac{450}{121} \bigg) = \bigg( \frac{450}{121} \bigg) \\ \\ \sf : \implies \: LHS = RHS$

$\therefore\</u><u>l</u><u>a</u><u>r</u><u>g</u><u>e</u><u> </u><u>{</u><u> \sf </u><u>{</u><u>T</u><u>h</u><u>e</u><u> </u><u>\</u><u>:</u><u>V</u><u>a</u><u>l</u><u>u</u><u>e</u><u>\</u><u>:</u><u>of \: x \: is \: \frac{15}{11}</u><u>}</u><u>}</u><u>$

$\huge \: \dag \: {\underline {\sf {</u><u>H</u><u>ence \: </u><u>V</u><u>erified}}}$