Solve for t 66=(t^2-t)/2

Math
66=t2-t2
Rewrite the equation as t2-t2=66.
t2-t2=66
Multiply both sides of the equation by 2.
2⋅t2-t2=2⋅66
Simplify both sides of the equation.
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Simplify 2⋅t2-t2.
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Simplify terms.
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Factor t out of t2-t.
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Factor t out of t2.
2⋅t⋅t-t2=2⋅66
Factor t out of -t.
2⋅t⋅t+t⋅-12=2⋅66
Factor t out of t⋅t+t⋅-1.
2⋅t(t-1)2=2⋅66
2⋅t(t-1)2=2⋅66
Cancel the common factor of 2.
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Cancel the common factor.
2⋅t(t-1)2=2⋅66
Rewrite the expression.
t(t-1)=2⋅66
t(t-1)=2⋅66
Apply the distributive property.
t⋅t+t⋅-1=2⋅66
Simplify the expression.
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Multiply t by t.
t2+t⋅-1=2⋅66
Move -1 to the left of t.
t2-1⋅t=2⋅66
t2-1⋅t=2⋅66
t2-1⋅t=2⋅66
Rewrite -1t as -t.
t2-t=2⋅66
t2-t=2⋅66
Multiply 2 by 66.
t2-t=132
t2-t=132
Move 132 to the left side of the equation by subtracting it from both sides.
t2-t-132=0
Factor t2-t-132 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -132 and whose sum is -1.
-12,11
Write the factored form using these integers.
(t-12)(t+11)=0
(t-12)(t+11)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
t-12=0
t+11=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
t-12=0
Add 12 to both sides of the equation.
t=12
t=12
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
t+11=0
Subtract 11 from both sides of the equation.
t=-11
t=-11
The final solution is all the values that make (t-12)(t+11)=0 true.
t=12,-11
Solve for t 66=(t^2-t)/2

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