# Solve for t 9=157-9t-16t^2 9=157-9t-16t2
Rewrite the equation as 157-9t-16t2=9.
157-9t-16t2=9
Move 9 to the left side of the equation by subtracting it from both sides.
157-9t-16t2-9=0
Subtract 9 from 157.
-9t-16t2+148=0
Factor -1 out of -9t-16t2+148.
Reorder -9t and -16t2.
-16t2-9t+148=0
Factor -1 out of -16t2.
-(16t2)-9t+148=0
Factor -1 out of -9t.
-(16t2)-(9t)+148=0
Rewrite 148 as -1(-148).
-(16t2)-(9t)-1⋅-148=0
Factor -1 out of -(16t2)-(9t).
-(16t2+9t)-1⋅-148=0
Factor -1 out of -(16t2+9t)-1(-148).
-(16t2+9t-148)=0
-(16t2+9t-148)=0
Multiply each term in -(16t2+9t-148)=0 by -1
Multiply each term in -(16t2+9t-148)=0 by -1.
-(16t2+9t-148)⋅-1=0⋅-1
Simplify -(16t2+9t-148)⋅-1.
Apply the distributive property.
(-(16t2)-(9t)–148)⋅-1=0⋅-1
Simplify.
Multiply 16 by -1.
(-16t2-(9t)–148)⋅-1=0⋅-1
Multiply 9 by -1.
(-16t2-9t–148)⋅-1=0⋅-1
Multiply -1 by -148.
(-16t2-9t+148)⋅-1=0⋅-1
(-16t2-9t+148)⋅-1=0⋅-1
Apply the distributive property.
-16t2⋅-1-9t⋅-1+148⋅-1=0⋅-1
Simplify.
Multiply -1 by -16.
16t2-9t⋅-1+148⋅-1=0⋅-1
Multiply -1 by -9.
16t2+9t+148⋅-1=0⋅-1
Multiply 148 by -1.
16t2+9t-148=0⋅-1
16t2+9t-148=0⋅-1
16t2+9t-148=0⋅-1
Multiply 0 by -1.
16t2+9t-148=0
16t2+9t-148=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=16, b=9, and c=-148 into the quadratic formula and solve for t.
-9±92-4⋅(16⋅-148)2⋅16
Simplify.
Simplify the numerator.
Raise 9 to the power of 2.
t=-9±81-4⋅(16⋅-148)2⋅16
Multiply 16 by -148.
t=-9±81-4⋅-23682⋅16
Multiply -4 by -2368.
t=-9±81+94722⋅16
Add 81 and 9472.
t=-9±95532⋅16
t=-9±95532⋅16
Multiply 2 by 16.
t=-9±955332
t=-9±955332
The final answer is the combination of both solutions.
t=-9-955332,-9+955332
The result can be shown in multiple forms.
Exact Form:
t=-9-955332,-9+955332
Decimal Form:
t=2.77310779…,-3.33560779…
Solve for t 9=157-9t-16t^2

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