GMAT Quadratic Equations: If x^2+b x+5=(x+c)^2 for all…

If x^{2} + b x + 5 = (x + c)^{2} for all numbers x, where b and c are positive constants, what is the value of b ?

quadratic equations

Explanation	Calculations	Help
$We expand the right-hand side to compare coefficients.$	$x^{2} + b x + 5 = x^{2} + 2 c x + c^{2}$
$We match the coefficient of x on both sides.$	$b = 2 c$
$We match the constant term on both sides.$	$c^{2} = 5$
$Since c is positive, we take the positive square root.$	$c = 5$
$We substitute c = 5 into b = 2 c .$	$b = 2 \times 5$

2 \sqrt5 (C)

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