13000000000=0.66t^2+2.49t+12.93

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Solution for 13000000000=0.66t^2+2.49t+12.93 equation:


Simplifying
13000000000 = 0.66t2 + 2.49t + 12.93

Reorder the terms:
13000000000 = 12.93 + 2.49t + 0.66t2

Solving
13000000000 = 12.93 + 2.49t + 0.66t2

Solving for variable 't'.

Combine like terms: 13000000000 + -12.93 = 12999999987.07
12999999987.07 + -2.49t + -0.66t2 = 12.93 + 2.49t + 0.66t2 + -12.93 + -2.49t + -0.66t2

Reorder the terms:
12999999987.07 + -2.49t + -0.66t2 = 12.93 + -12.93 + 2.49t + -2.49t + 0.66t2 + -0.66t2

Combine like terms: 12.93 + -12.93 = 0.00
12999999987.07 + -2.49t + -0.66t2 = 0.00 + 2.49t + -2.49t + 0.66t2 + -0.66t2
12999999987.07 + -2.49t + -0.66t2 = 2.49t + -2.49t + 0.66t2 + -0.66t2

Combine like terms: 2.49t + -2.49t = 0.00
12999999987.07 + -2.49t + -0.66t2 = 0.00 + 0.66t2 + -0.66t2
12999999987.07 + -2.49t + -0.66t2 = 0.66t2 + -0.66t2

Combine like terms: 0.66t2 + -0.66t2 = 0.00
12999999987.07 + -2.49t + -0.66t2 = 0.00

Begin completing the square.  Divide all terms by
-0.66 the coefficient of the squared term: 

Divide each side by '-0.66'.
-19696969680 + 3.772727273t + t2 = 0

Move the constant term to the right:

Add '19696969680' to each side of the equation.
-19696969680 + 3.772727273t + 19696969680 + t2 = 0 + 19696969680

Reorder the terms:
-19696969680 + 19696969680 + 3.772727273t + t2 = 0 + 19696969680

Combine like terms: -19696969680 + 19696969680 = 0
0 + 3.772727273t + t2 = 0 + 19696969680
3.772727273t + t2 = 0 + 19696969680

Combine like terms: 0 + 19696969680 = 19696969680
3.772727273t + t2 = 19696969680

The t term is 3.772727273t.  Take half its coefficient (1.886363637).
Square it (3.558367771) and add it to both sides.

Add '3.558367771' to each side of the equation.
3.772727273t + 3.558367771 + t2 = 19696969680 + 3.558367771

Reorder the terms:
3.558367771 + 3.772727273t + t2 = 19696969680 + 3.558367771

Combine like terms: 19696969680 + 3.558367771 = 19696969683.558367771
3.558367771 + 3.772727273t + t2 = 19696969683.558367771

Factor a perfect square on the left side:
(t + 1.886363637)(t + 1.886363637) = 19696969683.558367771

Calculate the square root of the right side: 140345.893005668

Break this problem into two subproblems by setting 
(t + 1.886363637) equal to 140345.893005668 and -140345.893005668.

Subproblem 1

t + 1.886363637 = 140345.893005668 Simplifying t + 1.886363637 = 140345.893005668 Reorder the terms: 1.886363637 + t = 140345.893005668 Solving 1.886363637 + t = 140345.893005668 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.886363637' to each side of the equation. 1.886363637 + -1.886363637 + t = 140345.893005668 + -1.886363637 Combine like terms: 1.886363637 + -1.886363637 = 0.000000000 0.000000000 + t = 140345.893005668 + -1.886363637 t = 140345.893005668 + -1.886363637 Combine like terms: 140345.893005668 + -1.886363637 = 140344.006642031 t = 140344.006642031 Simplifying t = 140344.006642031

Subproblem 2

t + 1.886363637 = -140345.893005668 Simplifying t + 1.886363637 = -140345.893005668 Reorder the terms: 1.886363637 + t = -140345.893005668 Solving 1.886363637 + t = -140345.893005668 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.886363637' to each side of the equation. 1.886363637 + -1.886363637 + t = -140345.893005668 + -1.886363637 Combine like terms: 1.886363637 + -1.886363637 = 0.000000000 0.000000000 + t = -140345.893005668 + -1.886363637 t = -140345.893005668 + -1.886363637 Combine like terms: -140345.893005668 + -1.886363637 = -140347.779369305 t = -140347.779369305 Simplifying t = -140347.779369305

Solution

The solution to the problem is based on the solutions from the subproblems. t = {140344.006642031, -140347.779369305}

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