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Simplifying 3t2 + 6t + -3 = 0 Reorder the terms: -3 + 6t + 3t2 = 0 Solving -3 + 6t + 3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 2t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 2t + t2)' equal to zero and attempt to solve: Simplifying -1 + 2t + t2 = 0 Solving -1 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 2t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + 2t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2t + t2 = 0 + 1 2t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 2t + t2 = 1 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 = 1 + 1 Reorder the terms: 1 + 2t + t2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2t + t2 = 2 Factor a perfect square on the left side: (t + 1)(t + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (t + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
t + 1 = 1.414213562 Simplifying t + 1 = 1.414213562 Reorder the terms: 1 + t = 1.414213562 Solving 1 + t = 1.414213562 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 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.414213562 + -1 t = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 t = 0.414213562 Simplifying t = 0.414213562Subproblem 2
t + 1 = -1.414213562 Simplifying t + 1 = -1.414213562 Reorder the terms: 1 + t = -1.414213562 Solving 1 + t = -1.414213562 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 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.414213562 + -1 t = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 t = -2.414213562 Simplifying t = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.414213562, -2.414213562}Solution
t = {0.414213562, -2.414213562}
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