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Simplifying 100 = 20t + 2t2 Solving 100 = 20t + 2t2 Solving for variable 't'. Reorder the terms: 100 + -20t + -2t2 = 20t + -20t + 2t2 + -2t2 Combine like terms: 20t + -20t = 0 100 + -20t + -2t2 = 0 + 2t2 + -2t2 100 + -20t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 100 + -20t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -10t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -10t + -1t2)' equal to zero and attempt to solve: Simplifying 50 + -10t + -1t2 = 0 Solving 50 + -10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + 10t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 10t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + 10t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 10t + t2 = 0 + 50 10t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 10t + t2 = 50 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = 50 + 25 Reorder the terms: 25 + 10t + t2 = 50 + 25 Combine like terms: 50 + 25 = 75 25 + 10t + t2 = 75 Factor a perfect square on the left side: (t + 5)(t + 5) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (t + 5) equal to 8.660254038 and -8.660254038.Subproblem 1
t + 5 = 8.660254038 Simplifying t + 5 = 8.660254038 Reorder the terms: 5 + t = 8.660254038 Solving 5 + t = 8.660254038 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 8.660254038 + -5 Combine like terms: 5 + -5 = 0 0 + t = 8.660254038 + -5 t = 8.660254038 + -5 Combine like terms: 8.660254038 + -5 = 3.660254038 t = 3.660254038 Simplifying t = 3.660254038Subproblem 2
t + 5 = -8.660254038 Simplifying t + 5 = -8.660254038 Reorder the terms: 5 + t = -8.660254038 Solving 5 + t = -8.660254038 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -8.660254038 + -5 Combine like terms: 5 + -5 = 0 0 + t = -8.660254038 + -5 t = -8.660254038 + -5 Combine like terms: -8.660254038 + -5 = -13.660254038 t = -13.660254038 Simplifying t = -13.660254038Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.660254038, -13.660254038}Solution
t = {3.660254038, -13.660254038}
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