Question

completing the square method x2+2x-5=0​

Answer 1

       $\huge{\underline{\bold{Solution:}}}$

       $\text{The given quadratic equation is }x^{2} + 2x - 5 = 0$

       $\text{Applying completing square method}$

$\implies \text{Adding }(1)^{2} \text{ and substracting }(1)^{2}$

$\implies x^{2} + 2x - 5 + 1 - 1 = 0$

       $\text{We know that, }(a+b)^{2} = a^{2} + b^{2} + 2ab$

$\implies (x+1)^{2} - 5 - 1 = 0$

$\implies (x+1)^{2} -6 = 0$

$\implies (x+1)^{2} - (\sqrt6)^{2} = 0$

       $\text{We know that, }(a+b)(a-b)= a^{2} - b^{2}$

$\implies (x+1+\sqrt6)(x+1-\sqrt6) = 0$

$\implies \{x + (1 + \sqrt6)\}\{x + (1-\sqrt6)\} = 0$

$\implies \boxed{x = -(1+\sqrt6),-(1-\sqrt6)}$