Say for positive quantities a, b, $a + b$ equals $a^2 + ab + b^2$. Choose the nearest value to b if a is given as 0.5.

Substituting $a = 0.5$ in $a + b = a^2 + ab + b^2$:

$0.5 + b = 0.25 + 0.5b + b^2$

$b^2 - 0.5b - 0.25 = 0$

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Applying the quadratic formula with $A = 1$, $B = -0.5$, $C = -0.25$:

$b = \dfrac{-(-0.5) \pm \sqrt{(-0.5)^2 - 4(1)(-0.25)}}{2(1)}$

$b = \dfrac{0.5 \pm \sqrt{0.25 + 1}}{2}$

$b = \dfrac{0.5 \pm \sqrt{1.25}}{2}$

$b = \dfrac{0.5 \pm 1.118}{2}$

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$b = \dfrac{0.5 + 1.118}{2} \approx 0.809$ or $b = \dfrac{0.5 - 1.118}{2} \approx -0.309$

Since $b$ is positive, $b \approx 0.809$, which is nearest to $0.8$.