Question

solve the following Quadratic equation by completing the square method ​

Answer 1

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➠ Solve the following Quadratic equation by completing the square method .

• 9x² - 8 = 2x

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❏ "Completing Square Method" is one of the most frequently used method to solve quadratic equations.

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❏ Here we add or subtract some terms to make perfect square and then get our answer.

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➠ Equation : 9x² - 8 = 2x

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Let's Start !

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First of all let's shift all terms on one side !

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$\bold { \orange { :\implies 9x^{2} - 2x - 8 = 0 }}$

$\bold { :\implies (3x)^{2} - 2(3x)(\dfrac{1}{3}) + \dfrac{1}{9} - 8 - \dfrac{1}{9} = 0 }$

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$\bold { :\implies (3x-\dfrac{1}{3})^2 - 8 - \dfrac{1}{9} = 0 }$

$\bold { :\implies (3x-\dfrac{1}{3})^2 = 8 + \dfrac{1}{9} }$

$\bold { :\implies (3x-\dfrac{1}{3})^2 = \dfrac{72 + 1}{9} }$

$\bold { :\implies (3x-\dfrac{1}{3})^2 = \dfrac{73}{9} }$

$\bold { :\implies 3x-\dfrac{1}{3} = \dfrac{\pm\sqrt{73}}{3} }$

$\bold { :\implies 3x = \dfrac{1 \pm \sqrt{73}}{3} }$

$\boxed { \bold {\red { :\implies x = \dfrac{1 \pm \sqrt{73}}{9} } } }$

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$\boxed{\boxed{\bold{\therefore Value\;of\; x = \dfrac{1 \pm \sqrt{73}}{9} }}}$

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Hope this helps u.../

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