How do you solve $sqrt(56-r)=r$ ?

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Answer 1 · 2016-12-19T15:43:54

$r = 7$

Square both sides to get

$56 - r = r^2$

Then gather terms to get

$r^2 + r - 56 = 0.$

This is a simple quadratic, which can be solved by the quadratic formula, or, more simply, by factoring, into

$(r - 7)(r +8) = 0$

Setting each factor equal to zero in turn gives

$r - 7 = 0 implies r = 8" "$ and $" "r + 8 = 0 implies r = -8$

To check,

$sqrt(56 - 7) = sqrt(49) = 7$

$sqrt(56 - (-8)) = sqrt(64) != -8 ->$ this means that $r=-8$ is not a solution to the original equation.

How do you solve sqrt(56-r)=rsqrt(56-r)=r?