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Simplifying t2 + -16t + 50 = 0 Reorder the terms: 50 + -16t + t2 = 0 Solving 50 + -16t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -16t + -50 + t2 = 0 + -50 Reorder the terms: 50 + -50 + -16t + t2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -16t + t2 = 0 + -50 -16t + t2 = 0 + -50 Combine like terms: 0 + -50 = -50 -16t + t2 = -50 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = -50 + 64 Reorder the terms: 64 + -16t + t2 = -50 + 64 Combine like terms: -50 + 64 = 14 64 + -16t + t2 = 14 Factor a perfect square on the left side: (t + -8)(t + -8) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (t + -8) equal to 3.741657387 and -3.741657387.Subproblem 1
t + -8 = 3.741657387 Simplifying t + -8 = 3.741657387 Reorder the terms: -8 + t = 3.741657387 Solving -8 + t = 3.741657387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 3.741657387 + 8 Combine like terms: -8 + 8 = 0 0 + t = 3.741657387 + 8 t = 3.741657387 + 8 Combine like terms: 3.741657387 + 8 = 11.741657387 t = 11.741657387 Simplifying t = 11.741657387Subproblem 2
t + -8 = -3.741657387 Simplifying t + -8 = -3.741657387 Reorder the terms: -8 + t = -3.741657387 Solving -8 + t = -3.741657387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -3.741657387 + 8 Combine like terms: -8 + 8 = 0 0 + t = -3.741657387 + 8 t = -3.741657387 + 8 Combine like terms: -3.741657387 + 8 = 4.258342613 t = 4.258342613 Simplifying t = 4.258342613Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.741657387, 4.258342613}
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