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