Math, asked by shidruksahil, 3 months ago

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

Answers

Answered by DeeznutzUwU
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)}

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