Question

Solve 2x²-5x-6=0 by use of completing square method

Answer 1

$2x^2-5x-6=0$

$2x^2-5x-6+6=0+6$

$2x^2-5x=6$

$\dfrac{2x^2-5x}{2}=\dfrac{6}{2}$

$x^2-\dfrac{5x}{2}=3$

$\left(x-\dfrac{5}{4}\right)^2=\dfrac{73}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$x=\dfrac{\sqrt{73}+5}{4},\:x=\dfrac{-\sqrt{73}+5}{4}$