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Simplifying 15t3 + 57t2 + -38t = 0 Reorder the terms: -38t + 57t2 + 15t3 = 0 Solving -38t + 57t2 + 15t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-38 + 57t + 15t2) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-38 + 57t + 15t2)' equal to zero and attempt to solve: Simplifying -38 + 57t + 15t2 = 0 Solving -38 + 57t + 15t2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.533333333 + 3.8t + t2 = 0 Move the constant term to the right: Add '2.533333333' to each side of the equation. -2.533333333 + 3.8t + 2.533333333 + t2 = 0 + 2.533333333 Reorder the terms: -2.533333333 + 2.533333333 + 3.8t + t2 = 0 + 2.533333333 Combine like terms: -2.533333333 + 2.533333333 = 0.000000000 0.000000000 + 3.8t + t2 = 0 + 2.533333333 3.8t + t2 = 0 + 2.533333333 Combine like terms: 0 + 2.533333333 = 2.533333333 3.8t + t2 = 2.533333333 The t term is 3.8t. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8t + 3.61 + t2 = 2.533333333 + 3.61 Reorder the terms: 3.61 + 3.8t + t2 = 2.533333333 + 3.61 Combine like terms: 2.533333333 + 3.61 = 6.143333333 3.61 + 3.8t + t2 = 6.143333333 Factor a perfect square on the left side: (t + 1.9)(t + 1.9) = 6.143333333 Calculate the square root of the right side: 2.478574859 Break this problem into two subproblems by setting (t + 1.9) equal to 2.478574859 and -2.478574859.Subproblem 1
t + 1.9 = 2.478574859 Simplifying t + 1.9 = 2.478574859 Reorder the terms: 1.9 + t = 2.478574859 Solving 1.9 + t = 2.478574859 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + t = 2.478574859 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + t = 2.478574859 + -1.9 t = 2.478574859 + -1.9 Combine like terms: 2.478574859 + -1.9 = 0.578574859 t = 0.578574859 Simplifying t = 0.578574859Subproblem 2
t + 1.9 = -2.478574859 Simplifying t + 1.9 = -2.478574859 Reorder the terms: 1.9 + t = -2.478574859 Solving 1.9 + t = -2.478574859 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + t = -2.478574859 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + t = -2.478574859 + -1.9 t = -2.478574859 + -1.9 Combine like terms: -2.478574859 + -1.9 = -4.378574859 t = -4.378574859 Simplifying t = -4.378574859Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.578574859, -4.378574859}Solution
t = {0, 0.578574859, -4.378574859}
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