What is the solution of t

Question

20=6+88t-16t²

Answer 1

First we want to get everything onto the same side of the equation so our equation is equal to 0:

20=6+88t-16t²

Subtract (6+88t-16t²) from both sides of the equation to get:

16t²-88t+14=0

Now simplify by pulling out a 2 from each term:

2(8t²-44t+7)=0

Divide both sides by 2:

8t²-44t+7=0

Now use the quadratic formula to solve for t:

x=-b±√b²-4ac

2a

=44±√1936-4*8*7

2*8

=44±√1712

16

=44±4√107

16

=11±√107

4

The Correct Answer is: 11±√107

4

Answer 2

Simplify:

20 = 6 + 88t - 16t²

0 = -14 + 88t - 16t²

0 = 16t² - 88t + 14

0 = 8t² - 44t + 7

Use the quadratic formula to solve for t:

t = [44 ± √((-44)² - 4(8)(7))] / (2*8) = (44 ± √1712) / 16 = 5.34, 0.16

Answer 3

The typical method of solving a quadratic is to first set it equal to zero and then either use factoring or the quadratic formula to solve. So, subtracting 20 from both sides gives us:

-16t² + 88t - 14 = 0

We can now simplify by dividing everything by -2 to get:

8t² - 44t + 7 = 0

I don't see a way to factor, so we will use the quadratic formula. It says, for at² + bt + c = 0,

t = [-b ± √(b² - 4ac)]/(2a)

a = 8, b = -44, c = 7 so:

t = [44 ± √(44² - 4(8)(7))]/(2(8))

t = [44 ± √(1936-224)]/16

t = [44 ± √1712]/16

t = [44 ± 4√107]/16

t = [11 ± √107]/4

An approximate answer can be attained using a calculator to get a numeric value for √107. t ≈ 0.164 and t ≈ 5.336