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Simplifying -60 = 5.13t + -5t2 Solving -60 = 5.13t + -5t2 Solving for variable 't'. Reorder the terms: -60 + -5.13t + 5t2 = 5.13t + -5.13t + -5t2 + 5t2 Combine like terms: 5.13t + -5.13t = 0.00 -60 + -5.13t + 5t2 = 0.00 + -5t2 + 5t2 -60 + -5.13t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -60 + -5.13t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12 + -1.026t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -1.026t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -1.026t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1.026t + t2 = 0 + 12 -1.026t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -1.026t + t2 = 12 The t term is -1.026t. Take half its coefficient (-0.513). Square it (0.263169) and add it to both sides. Add '0.263169' to each side of the equation. -1.026t + 0.263169 + t2 = 12 + 0.263169 Reorder the terms: 0.263169 + -1.026t + t2 = 12 + 0.263169 Combine like terms: 12 + 0.263169 = 12.263169 0.263169 + -1.026t + t2 = 12.263169 Factor a perfect square on the left side: (t + -0.513)(t + -0.513) = 12.263169 Calculate the square root of the right side: 3.50188078 Break this problem into two subproblems by setting (t + -0.513) equal to 3.50188078 and -3.50188078.Subproblem 1
t + -0.513 = 3.50188078 Simplifying t + -0.513 = 3.50188078 Reorder the terms: -0.513 + t = 3.50188078 Solving -0.513 + t = 3.50188078 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.513' to each side of the equation. -0.513 + 0.513 + t = 3.50188078 + 0.513 Combine like terms: -0.513 + 0.513 = 0.000 0.000 + t = 3.50188078 + 0.513 t = 3.50188078 + 0.513 Combine like terms: 3.50188078 + 0.513 = 4.01488078 t = 4.01488078 Simplifying t = 4.01488078Subproblem 2
t + -0.513 = -3.50188078 Simplifying t + -0.513 = -3.50188078 Reorder the terms: -0.513 + t = -3.50188078 Solving -0.513 + t = -3.50188078 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.513' to each side of the equation. -0.513 + 0.513 + t = -3.50188078 + 0.513 Combine like terms: -0.513 + 0.513 = 0.000 0.000 + t = -3.50188078 + 0.513 t = -3.50188078 + 0.513 Combine like terms: -3.50188078 + 0.513 = -2.98888078 t = -2.98888078 Simplifying t = -2.98888078Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.01488078, -2.98888078}
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