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Simplifying 1.85t2 + 50t = 1 Reorder the terms: 50t + 1.85t2 = 1 Solving 50t + 1.85t2 = 1 Solving for variable 't'. Reorder the terms: -1 + 50t + 1.85t2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 50t + 1.85t2 = 0 Begin completing the square. Divide all terms by 1.85 the coefficient of the squared term: Divide each side by '1.85'. -0.5405405405 + 27.02702703t + t2 = 0 Move the constant term to the right: Add '0.5405405405' to each side of the equation. -0.5405405405 + 27.02702703t + 0.5405405405 + t2 = 0 + 0.5405405405 Reorder the terms: -0.5405405405 + 0.5405405405 + 27.02702703t + t2 = 0 + 0.5405405405 Combine like terms: -0.5405405405 + 0.5405405405 = 0.0000000000 0.0000000000 + 27.02702703t + t2 = 0 + 0.5405405405 27.02702703t + t2 = 0 + 0.5405405405 Combine like terms: 0 + 0.5405405405 = 0.5405405405 27.02702703t + t2 = 0.5405405405 The t term is 27.02702703t. Take half its coefficient (13.51351352). Square it (182.6150477) and add it to both sides. Add '182.6150477' to each side of the equation. 27.02702703t + 182.6150477 + t2 = 0.5405405405 + 182.6150477 Reorder the terms: 182.6150477 + 27.02702703t + t2 = 0.5405405405 + 182.6150477 Combine like terms: 0.5405405405 + 182.6150477 = 183.1555882405 182.6150477 + 27.02702703t + t2 = 183.1555882405 Factor a perfect square on the left side: (t + 13.51351352)(t + 13.51351352) = 183.1555882405 Calculate the square root of the right side: 13.533498744 Break this problem into two subproblems by setting (t + 13.51351352) equal to 13.533498744 and -13.533498744.Subproblem 1
t + 13.51351352 = 13.533498744 Simplifying t + 13.51351352 = 13.533498744 Reorder the terms: 13.51351352 + t = 13.533498744 Solving 13.51351352 + t = 13.533498744 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-13.51351352' to each side of the equation. 13.51351352 + -13.51351352 + t = 13.533498744 + -13.51351352 Combine like terms: 13.51351352 + -13.51351352 = 0.00000000 0.00000000 + t = 13.533498744 + -13.51351352 t = 13.533498744 + -13.51351352 Combine like terms: 13.533498744 + -13.51351352 = 0.019985224 t = 0.019985224 Simplifying t = 0.019985224Subproblem 2
t + 13.51351352 = -13.533498744 Simplifying t + 13.51351352 = -13.533498744 Reorder the terms: 13.51351352 + t = -13.533498744 Solving 13.51351352 + t = -13.533498744 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-13.51351352' to each side of the equation. 13.51351352 + -13.51351352 + t = -13.533498744 + -13.51351352 Combine like terms: 13.51351352 + -13.51351352 = 0.00000000 0.00000000 + t = -13.533498744 + -13.51351352 t = -13.533498744 + -13.51351352 Combine like terms: -13.533498744 + -13.51351352 = -27.047012264 t = -27.047012264 Simplifying t = -27.047012264Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.019985224, -27.047012264}
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