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

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.

-(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 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