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Simplifying 10 = 20t + -2t2 Solving 10 = 20t + -2t2 Solving for variable 't'. Reorder the terms: 10 + -20t + 2t2 = 20t + -20t + -2t2 + 2t2 Combine like terms: 20t + -20t = 0 10 + -20t + 2t2 = 0 + -2t2 + 2t2 10 + -20t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 10 + -20t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -10t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -10t + t2)' equal to zero and attempt to solve: Simplifying 5 + -10t + t2 = 0 Solving 5 + -10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -10t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -10t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -10t + t2 = 0 + -5 -10t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -10t + t2 = -5 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 = -5 + 25 Reorder the terms: 25 + -10t + t2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + -10t + t2 = 20 Factor a perfect square on the left side: (t + -5)(t + -5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (t + -5) equal to 4.472135955 and -4.472135955.Subproblem 1
t + -5 = 4.472135955 Simplifying t + -5 = 4.472135955 Reorder the terms: -5 + t = 4.472135955 Solving -5 + t = 4.472135955 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 = 4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + t = 4.472135955 + 5 t = 4.472135955 + 5 Combine like terms: 4.472135955 + 5 = 9.472135955 t = 9.472135955 Simplifying t = 9.472135955Subproblem 2
t + -5 = -4.472135955 Simplifying t + -5 = -4.472135955 Reorder the terms: -5 + t = -4.472135955 Solving -5 + t = -4.472135955 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 = -4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + t = -4.472135955 + 5 t = -4.472135955 + 5 Combine like terms: -4.472135955 + 5 = 0.527864045 t = 0.527864045 Simplifying t = 0.527864045Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.472135955, 0.527864045}Solution
t = {9.472135955, 0.527864045}
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