# Solve for t -16t^2-22t+100=0

-16t2-22t+100=0
Factor -2 out of -16t2-22t+100.
Factor -2 out of -16t2.
-2(8t2)-22t+100=0
Factor -2 out of -22t.
-2(8t2)-2(11t)+100=0
Factor -2 out of 100.
-2(8t2)-2(11t)-2⋅-50=0
Factor -2 out of -2(8t2)-2(11t).
-2(8t2+11t)-2⋅-50=0
Factor -2 out of -2(8t2+11t)-2(-50).
-2(8t2+11t-50)=0
-2(8t2+11t-50)=0
Divide each term by -2 and simplify.
Divide each term in -2(8t2+11t-50)=0 by -2.
-2(8t2+11t-50)-2=0-2
Cancel the common factor of -2.
Cancel the common factor.
-2(8t2+11t-50)-2=0-2
Divide 8t2+11t-50 by 1.
8t2+11t-50=0-2
8t2+11t-50=0-2
Divide 0 by -2.
8t2+11t-50=0
8t2+11t-50=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=8, b=11, and c=-50 into the quadratic formula and solve for t.
-11±112-4⋅(8⋅-50)2⋅8
Simplify.
Simplify the numerator.
Raise 11 to the power of 2.
t=-11±121-4⋅(8⋅-50)2⋅8
Multiply 8 by -50.
t=-11±121-4⋅-4002⋅8
Multiply -4 by -400.
t=-11±121+16002⋅8
t=-11±17212⋅8
t=-11±17212⋅8
Multiply 2 by 8.
t=-11±172116
t=-11±172116
The final answer is the combination of both solutions.
t=-11-172116,-11+172116
The result can be shown in multiple forms.
Exact Form:
t=-11-172116,-11+172116
Decimal Form:
t=1.90530856…,-3.28030856…
Solve for t -16t^2-22t+100=0

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