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Simplifying 2 = 16t2 + 100t + 4 Reorder the terms: 2 = 4 + 100t + 16t2 Solving 2 = 4 + 100t + 16t2 Solving for variable 't'. Combine like terms: 2 + -4 = -2 -2 + -100t + -16t2 = 4 + 100t + 16t2 + -4 + -100t + -16t2 Reorder the terms: -2 + -100t + -16t2 = 4 + -4 + 100t + -100t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -2 + -100t + -16t2 = 0 + 100t + -100t + 16t2 + -16t2 -2 + -100t + -16t2 = 100t + -100t + 16t2 + -16t2 Combine like terms: 100t + -100t = 0 -2 + -100t + -16t2 = 0 + 16t2 + -16t2 -2 + -100t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -2 + -100t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + 50t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + 50t + 8t2)' equal to zero and attempt to solve: Simplifying 1 + 50t + 8t2 = 0 Solving 1 + 50t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 6.25t + t2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 6.25t + -0.125 + t2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 6.25t + t2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 6.25t + t2 = 0 + -0.125 6.25t + t2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 6.25t + t2 = -0.125 The t term is 6.25t. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25t + 9.765625 + t2 = -0.125 + 9.765625 Reorder the terms: 9.765625 + 6.25t + t2 = -0.125 + 9.765625 Combine like terms: -0.125 + 9.765625 = 9.640625 9.765625 + 6.25t + t2 = 9.640625 Factor a perfect square on the left side: (t + 3.125)(t + 3.125) = 9.640625 Calculate the square root of the right side: 3.104935587 Break this problem into two subproblems by setting (t + 3.125) equal to 3.104935587 and -3.104935587.Subproblem 1
t + 3.125 = 3.104935587 Simplifying t + 3.125 = 3.104935587 Reorder the terms: 3.125 + t = 3.104935587 Solving 3.125 + t = 3.104935587 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + t = 3.104935587 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + t = 3.104935587 + -3.125 t = 3.104935587 + -3.125 Combine like terms: 3.104935587 + -3.125 = -0.020064413 t = -0.020064413 Simplifying t = -0.020064413Subproblem 2
t + 3.125 = -3.104935587 Simplifying t + 3.125 = -3.104935587 Reorder the terms: 3.125 + t = -3.104935587 Solving 3.125 + t = -3.104935587 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + t = -3.104935587 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + t = -3.104935587 + -3.125 t = -3.104935587 + -3.125 Combine like terms: -3.104935587 + -3.125 = -6.229935587 t = -6.229935587 Simplifying t = -6.229935587Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.020064413, -6.229935587}Solution
t = {-0.020064413, -6.229935587}
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