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Simplifying 22 + 15t = 3.02t2 + -6.0 Reorder the terms: 22 + 15t = -6.0 + 3.02t2 Solving 22 + 15t = -6.0 + 3.02t2 Solving for variable 't'. Reorder the terms: 22 + 6.0 + 15t + -3.02t2 = -6.0 + 3.02t2 + 6.0 + -3.02t2 Combine like terms: 22 + 6.0 = 28 28 + 15t + -3.02t2 = -6.0 + 3.02t2 + 6.0 + -3.02t2 Reorder the terms: 28 + 15t + -3.02t2 = -6.0 + 6.0 + 3.02t2 + -3.02t2 Combine like terms: -6.0 + 6.0 = 0.0 28 + 15t + -3.02t2 = 0.0 + 3.02t2 + -3.02t2 28 + 15t + -3.02t2 = 3.02t2 + -3.02t2 Combine like terms: 3.02t2 + -3.02t2 = 0.00 28 + 15t + -3.02t2 = 0.00 Begin completing the square. Divide all terms by -3.02 the coefficient of the squared term: Divide each side by '-3.02'. -9.271523179 + -4.966887417t + t2 = 0 Move the constant term to the right: Add '9.271523179' to each side of the equation. -9.271523179 + -4.966887417t + 9.271523179 + t2 = 0 + 9.271523179 Reorder the terms: -9.271523179 + 9.271523179 + -4.966887417t + t2 = 0 + 9.271523179 Combine like terms: -9.271523179 + 9.271523179 = 0.000000000 0.000000000 + -4.966887417t + t2 = 0 + 9.271523179 -4.966887417t + t2 = 0 + 9.271523179 Combine like terms: 0 + 9.271523179 = 9.271523179 -4.966887417t + t2 = 9.271523179 The t term is -4.966887417t. Take half its coefficient (-2.483443709). Square it (6.167492656) and add it to both sides. Add '6.167492656' to each side of the equation. -4.966887417t + 6.167492656 + t2 = 9.271523179 + 6.167492656 Reorder the terms: 6.167492656 + -4.966887417t + t2 = 9.271523179 + 6.167492656 Combine like terms: 9.271523179 + 6.167492656 = 15.439015835 6.167492656 + -4.966887417t + t2 = 15.439015835 Factor a perfect square on the left side: (t + -2.483443709)(t + -2.483443709) = 15.439015835 Calculate the square root of the right side: 3.929251307 Break this problem into two subproblems by setting (t + -2.483443709) equal to 3.929251307 and -3.929251307.Subproblem 1
t + -2.483443709 = 3.929251307 Simplifying t + -2.483443709 = 3.929251307 Reorder the terms: -2.483443709 + t = 3.929251307 Solving -2.483443709 + t = 3.929251307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.483443709' to each side of the equation. -2.483443709 + 2.483443709 + t = 3.929251307 + 2.483443709 Combine like terms: -2.483443709 + 2.483443709 = 0.000000000 0.000000000 + t = 3.929251307 + 2.483443709 t = 3.929251307 + 2.483443709 Combine like terms: 3.929251307 + 2.483443709 = 6.412695016 t = 6.412695016 Simplifying t = 6.412695016Subproblem 2
t + -2.483443709 = -3.929251307 Simplifying t + -2.483443709 = -3.929251307 Reorder the terms: -2.483443709 + t = -3.929251307 Solving -2.483443709 + t = -3.929251307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.483443709' to each side of the equation. -2.483443709 + 2.483443709 + t = -3.929251307 + 2.483443709 Combine like terms: -2.483443709 + 2.483443709 = 0.000000000 0.000000000 + t = -3.929251307 + 2.483443709 t = -3.929251307 + 2.483443709 Combine like terms: -3.929251307 + 2.483443709 = -1.445807598 t = -1.445807598 Simplifying t = -1.445807598Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.412695016, -1.445807598}
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