Question

2X2-11x+5=0by completing square methid

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Solution :-

Given Polynomial

→ 2x² - 11x + 5 = 0

Now in first step we will divide both sides by 2

$\rightarrow \dfrac{2x^2 - 11x + 5}{2} = \dfrac{0}{2}$

$\rightarrow x^2 - \dfrac{11}{2}x + \dfrac{5}{2} = 0$

Now we will send the constant term to right side :-

$\rightarrow x^2 - \dfrac{11}{2}x = \dfrac{-5}{2}$

Now we will add $\bold{\underline{(\frac{11}{4})^2}}$ to both sides

$\rightarrow x^2 - \dfrac{11}{2}x +\left(\dfrac{11}{4}\right)^2 = \dfrac{-5}{2} + \left(\dfrac{11}{4}\right)^2$

$\rightarrow x^2 - \dfrac{11}{2}x + \dfrac{121}{16} =\dfrac{-5}{2}+\dfrac{121}{16}$

$\rightarrow \left( x - \dfrac{11}{4}\right)^2 = \dfrac{121 - 40}{16}$

$\rightarrow \left( x - \dfrac{11}{4}\right)^2 = \dfrac{81}{16}$

Taking square root both sides :-

$\rightarrow \left( x - \dfrac{11}{4}\right) = \pm\dfrac{9}{4}$

$\rightarrow x = \pm \dfrac{9}{4} + \dfrac{11}{4}$

$\rightarrow x = \dfrac{11 - 9}{4} \: and \: \dfrac{11 + 9}{4}$

$\rightarrow x = \dfrac{2}{4} \: and \: \dfrac{20}{4}$

So Value of x

$\huge{\boxed{\sf{ = \dfrac{1}{2} \: and \: 5 }}}$