How do you solve sqrt(56-r)=r√56−r=r?
1 Answer
Explanation:
Square both sides to get
56 - r = r^256−r=r2
Then gather terms to get
r^2 + r - 56 = 0.r2+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(r−7)(r+8)=0
Setting each factor equal to zero in turn gives
r - 7 = 0 implies r = 8" "r−7=0⇒r=8 and" "r + 8 = 0 implies r = -8 r+8=0⇒r=−8
To check,
sqrt(56 - 7) = sqrt(49) = 7√56−7=√49=7
sqrt(56 - (-8)) = sqrt(64) != -8 ->√56−(−8)=√64≠−8→ this means thatr=-8r=−8 is not a solution to the original equation.
