0=-16t^2+15t+100

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Solution for 0=-16t^2+15t+100 equation:


Simplifying
0 = -16t2 + 15t + 100

Reorder the terms:
0 = 100 + 15t + -16t2

Solving
0 = 100 + 15t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -100 = -100
-100 + -15t + 16t2 = 100 + 15t + -16t2 + -100 + -15t + 16t2

Reorder the terms:
-100 + -15t + 16t2 = 100 + -100 + 15t + -15t + -16t2 + 16t2

Combine like terms: 100 + -100 = 0
-100 + -15t + 16t2 = 0 + 15t + -15t + -16t2 + 16t2
-100 + -15t + 16t2 = 15t + -15t + -16t2 + 16t2

Combine like terms: 15t + -15t = 0
-100 + -15t + 16t2 = 0 + -16t2 + 16t2
-100 + -15t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-100 + -15t + 16t2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
-6.25 + -0.9375t + t2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -0.9375t + 6.25 + t2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -0.9375t + t2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -0.9375t + t2 = 0 + 6.25
-0.9375t + t2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-0.9375t + t2 = 6.25

The t term is -0.9375t.  Take half its coefficient (-0.46875).
Square it (0.2197265625) and add it to both sides.

Add '0.2197265625' to each side of the equation.
-0.9375t + 0.2197265625 + t2 = 6.25 + 0.2197265625

Reorder the terms:
0.2197265625 + -0.9375t + t2 = 6.25 + 0.2197265625

Combine like terms: 6.25 + 0.2197265625 = 6.4697265625
0.2197265625 + -0.9375t + t2 = 6.4697265625

Factor a perfect square on the left side:
(t + -0.46875)(t + -0.46875) = 6.4697265625

Calculate the square root of the right side: 2.543565718

Break this problem into two subproblems by setting 
(t + -0.46875) equal to 2.543565718 and -2.543565718.

Subproblem 1

t + -0.46875 = 2.543565718 Simplifying t + -0.46875 = 2.543565718 Reorder the terms: -0.46875 + t = 2.543565718 Solving -0.46875 + t = 2.543565718 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = 2.543565718 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 2.543565718 + 0.46875 t = 2.543565718 + 0.46875 Combine like terms: 2.543565718 + 0.46875 = 3.012315718 t = 3.012315718 Simplifying t = 3.012315718

Subproblem 2

t + -0.46875 = -2.543565718 Simplifying t + -0.46875 = -2.543565718 Reorder the terms: -0.46875 + t = -2.543565718 Solving -0.46875 + t = -2.543565718 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = -2.543565718 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -2.543565718 + 0.46875 t = -2.543565718 + 0.46875 Combine like terms: -2.543565718 + 0.46875 = -2.074815718 t = -2.074815718 Simplifying t = -2.074815718

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.012315718, -2.074815718}

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