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Simplifying 0 = -16t2 + 59t + 6 Reorder the terms: 0 = 6 + 59t + -16t2 Solving 0 = 6 + 59t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -59t + 16t2 = 6 + 59t + -16t2 + -6 + -59t + 16t2 Reorder the terms: -6 + -59t + 16t2 = 6 + -6 + 59t + -59t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -59t + 16t2 = 0 + 59t + -59t + -16t2 + 16t2 -6 + -59t + 16t2 = 59t + -59t + -16t2 + 16t2 Combine like terms: 59t + -59t = 0 -6 + -59t + 16t2 = 0 + -16t2 + 16t2 -6 + -59t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -59t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.375 + -3.6875t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3.6875t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3.6875t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3.6875t + t2 = 0 + 0.375 -3.6875t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3.6875t + t2 = 0.375 The t term is -3.6875t. Take half its coefficient (-1.84375). Square it (3.399414063) and add it to both sides. Add '3.399414063' to each side of the equation. -3.6875t + 3.399414063 + t2 = 0.375 + 3.399414063 Reorder the terms: 3.399414063 + -3.6875t + t2 = 0.375 + 3.399414063 Combine like terms: 0.375 + 3.399414063 = 3.774414063 3.399414063 + -3.6875t + t2 = 3.774414063 Factor a perfect square on the left side: (t + -1.84375)(t + -1.84375) = 3.774414063 Calculate the square root of the right side: 1.94278513 Break this problem into two subproblems by setting (t + -1.84375) equal to 1.94278513 and -1.94278513.Subproblem 1
t + -1.84375 = 1.94278513 Simplifying t + -1.84375 = 1.94278513 Reorder the terms: -1.84375 + t = 1.94278513 Solving -1.84375 + t = 1.94278513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.84375' to each side of the equation. -1.84375 + 1.84375 + t = 1.94278513 + 1.84375 Combine like terms: -1.84375 + 1.84375 = 0.00000 0.00000 + t = 1.94278513 + 1.84375 t = 1.94278513 + 1.84375 Combine like terms: 1.94278513 + 1.84375 = 3.78653513 t = 3.78653513 Simplifying t = 3.78653513Subproblem 2
t + -1.84375 = -1.94278513 Simplifying t + -1.84375 = -1.94278513 Reorder the terms: -1.84375 + t = -1.94278513 Solving -1.84375 + t = -1.94278513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.84375' to each side of the equation. -1.84375 + 1.84375 + t = -1.94278513 + 1.84375 Combine like terms: -1.84375 + 1.84375 = 0.00000 0.00000 + t = -1.94278513 + 1.84375 t = -1.94278513 + 1.84375 Combine like terms: -1.94278513 + 1.84375 = -0.09903513 t = -0.09903513 Simplifying t = -0.09903513Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.78653513, -0.09903513}
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