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Simplifying -2t + 3t3 + -5t + 6t2 = 0 Reorder the terms: -2t + -5t + 6t2 + 3t3 = 0 Combine like terms: -2t + -5t = -7t -7t + 6t2 + 3t3 = 0 Solving -7t + 6t2 + 3t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-7 + 6t + 3t2) = 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 '(-7 + 6t + 3t2)' equal to zero and attempt to solve: Simplifying -7 + 6t + 3t2 = 0 Solving -7 + 6t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 2t + t2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 2t + 2.333333333 + t2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 2t + t2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 2t + t2 = 0 + 2.333333333 2t + t2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 2t + t2 = 2.333333333 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 2.333333333 + 1 Reorder the terms: 1 + 2t + t2 = 2.333333333 + 1 Combine like terms: 2.333333333 + 1 = 3.333333333 1 + 2t + t2 = 3.333333333 Factor a perfect square on the left side: (t + 1)(t + 1) = 3.333333333 Calculate the square root of the right side: 1.825741858 Break this problem into two subproblems by setting (t + 1) equal to 1.825741858 and -1.825741858.Subproblem 1
t + 1 = 1.825741858 Simplifying t + 1 = 1.825741858 Reorder the terms: 1 + t = 1.825741858 Solving 1 + t = 1.825741858 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 1.825741858 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.825741858 + -1 t = 1.825741858 + -1 Combine like terms: 1.825741858 + -1 = 0.825741858 t = 0.825741858 Simplifying t = 0.825741858Subproblem 2
t + 1 = -1.825741858 Simplifying t + 1 = -1.825741858 Reorder the terms: 1 + t = -1.825741858 Solving 1 + t = -1.825741858 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -1.825741858 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.825741858 + -1 t = -1.825741858 + -1 Combine like terms: -1.825741858 + -1 = -2.825741858 t = -2.825741858 Simplifying t = -2.825741858Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.825741858, -2.825741858}Solution
t = {0, 0.825741858, -2.825741858}
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