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

##### 1 Answer

#### Answer:

#### Explanation:

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# isnota solution to the original equation.