Complete the square

t^2+10t=75

t^2+10t=75

COMPLETING THE SQUARE (PROCESS):

Do a reverse factoring procedure to develop the following form of equation:

(t + a)^2 = b

where:

t = unknown variable

a = coefficient

b = coefficient

Then 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 = √100

Two solutions exist:

+(t + 5) = 10

AND

-(t + 5) = 10

Thus:

t = 10 - 5 = 5

AND

t = -5 - 10 = -15

Answer:

t = 5

AND

t = -15

\( t^2+10t=75 \\ t^2+10t+25-25=75\\ (t+5)^2=100\\ |t+5|=10\\ t+5=10 \vee t+5=-10\\ t=5 \vee t=-15 \)

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