(4x+2)√(x^2+x+1) =4x√(x^2+x+1)+2√(x^2+x+1) =2√(x^2+x+1)(2x+1) =2(2x+1)√(x^2+x+1) ...

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Solving a Quadratic Equation by Completion of Squares Method

Solve: 4x+2√...

Question

Solve:
$(4 x + 2) \sqrt{x^{2} + x + 1}$

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Solution

$(4 x + 2) \sqrt{x^{2} + x + 1}$

$= 4 x \sqrt{x^{2} + x + 1} + 2 \sqrt{x^{2} + x + 1}$

$= 2 \sqrt{x^{2} + x + 1} (2 x + 1)$

$= 2 (2 x + 1) \sqrt{x^{2} + x + 1}$

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