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Simplifying 5t(8 + -1t) = -20 (8 * 5t + -1t * 5t) = -20 (40t + -5t2) = -20 Solving 40t + -5t2 = -20 Solving for variable 't'. Reorder the terms: 20 + 40t + -5t2 = -20 + 20 Combine like terms: -20 + 20 = 0 20 + 40t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(4 + 8t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + 8t + -1t2)' equal to zero and attempt to solve: Simplifying 4 + 8t + -1t2 = 0 Solving 4 + 8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -8t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -8t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -8t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8t + t2 = 0 + 4 -8t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8t + t2 = 4 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 4 + 16 Reorder the terms: 16 + -8t + t2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + -8t + t2 = 20 Factor a perfect square on the left side: (t + -4)(t + -4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (t + -4) equal to 4.472135955 and -4.472135955.Subproblem 1
t + -4 = 4.472135955 Simplifying t + -4 = 4.472135955 Reorder the terms: -4 + t = 4.472135955 Solving -4 + t = 4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.472135955 + 4 t = 4.472135955 + 4 Combine like terms: 4.472135955 + 4 = 8.472135955 t = 8.472135955 Simplifying t = 8.472135955Subproblem 2
t + -4 = -4.472135955 Simplifying t + -4 = -4.472135955 Reorder the terms: -4 + t = -4.472135955 Solving -4 + t = -4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.472135955 + 4 t = -4.472135955 + 4 Combine like terms: -4.472135955 + 4 = -0.472135955 t = -0.472135955 Simplifying t = -0.472135955Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.472135955, -0.472135955}Solution
t = {8.472135955, -0.472135955}
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