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Simplifying 2t2 + 6t + 2 = 0 Reorder the terms: 2 + 6t + 2t2 = 0 Solving 2 + 6t + 2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 3t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 3t + t2)' equal to zero and attempt to solve: Simplifying 1 + 3t + t2 = 0 Solving 1 + 3t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + 3t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3t + t2 = 0 + -1 3t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 3t + t2 = -1 The t term is 3t. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3t + 2.25 + t2 = -1 + 2.25 Reorder the terms: 2.25 + 3t + t2 = -1 + 2.25 Combine like terms: -1 + 2.25 = 1.25 2.25 + 3t + t2 = 1.25 Factor a perfect square on the left side: (t + 1.5)(t + 1.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (t + 1.5) equal to 1.118033989 and -1.118033989.Subproblem 1
t + 1.5 = 1.118033989 Simplifying t + 1.5 = 1.118033989 Reorder the terms: 1.5 + t = 1.118033989 Solving 1.5 + t = 1.118033989 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = 1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 1.118033989 + -1.5 t = 1.118033989 + -1.5 Combine like terms: 1.118033989 + -1.5 = -0.381966011 t = -0.381966011 Simplifying t = -0.381966011Subproblem 2
t + 1.5 = -1.118033989 Simplifying t + 1.5 = -1.118033989 Reorder the terms: 1.5 + t = -1.118033989 Solving 1.5 + t = -1.118033989 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = -1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -1.118033989 + -1.5 t = -1.118033989 + -1.5 Combine like terms: -1.118033989 + -1.5 = -2.618033989 t = -2.618033989 Simplifying t = -2.618033989Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.381966011, -2.618033989}Solution
t = {-0.381966011, -2.618033989}
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