Accepted Answer
COMPLETING THE SQUARE (PROCESS):Do a reverse factoring procedure to develop the following form of equation:(t + a)^2 = bwhere: t = unknown variable a = coefficient b = coefficientThen take square root of both sides to find value of unknown variable as follows:t^2 + 10t = 75(t^2 + 10t + 25) = 75 + 25(t^2 + 5t + 5t + 25) = 100(t + 5)(t + 5) = 100(t + 5)^2 = 100√(t + 5)^2 = √100Two solutions exist:+(t + 5) = 10AND-(t + 5) = 10Thus:t = 10 - 5 = 5ANDt = -5 - 10 = -15Answer:t = 5ANDt = -15
Suggested Answer
[tex] t^2+10t=75 \\
t^2+10t+25-25=75\\
(t+5)^2=100\\
|t+5|=10\\
t+5=10 \vee t+5=-10\\
t=5 \vee t=-15[/tex]