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Simplifying 2t2 + 8t + 2 = 0 Reorder the terms: 2 + 8t + 2t2 = 0 Solving 2 + 8t + 2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 4t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 4t + t2)' equal to zero and attempt to solve: Simplifying 1 + 4t + t2 = 0 Solving 1 + 4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + 4t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4t + t2 = 0 + -1 4t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 4t + t2 = -1 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = -1 + 4 Reorder the terms: 4 + 4t + t2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + 4t + t2 = 3 Factor a perfect square on the left side: (t + 2)(t + 2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (t + 2) equal to 1.732050808 and -1.732050808.Subproblem 1
t + 2 = 1.732050808 Simplifying t + 2 = 1.732050808 Reorder the terms: 2 + t = 1.732050808 Solving 2 + t = 1.732050808 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + t = 1.732050808 + -2 t = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 t = -0.267949192 Simplifying t = -0.267949192Subproblem 2
t + 2 = -1.732050808 Simplifying t + 2 = -1.732050808 Reorder the terms: 2 + t = -1.732050808 Solving 2 + t = -1.732050808 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + t = -1.732050808 + -2 t = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 t = -3.732050808 Simplifying t = -3.732050808Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.267949192, -3.732050808}Solution
t = {-0.267949192, -3.732050808}
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