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Simplifying 63 = -0.24t2 + 3.2t + 60 Reorder the terms: 63 = 60 + 3.2t + -0.24t2 Solving 63 = 60 + 3.2t + -0.24t2 Solving for variable 't'. Combine like terms: 63 + -60 = 3 3 + -3.2t + 0.24t2 = 60 + 3.2t + -0.24t2 + -60 + -3.2t + 0.24t2 Reorder the terms: 3 + -3.2t + 0.24t2 = 60 + -60 + 3.2t + -3.2t + -0.24t2 + 0.24t2 Combine like terms: 60 + -60 = 0 3 + -3.2t + 0.24t2 = 0 + 3.2t + -3.2t + -0.24t2 + 0.24t2 3 + -3.2t + 0.24t2 = 3.2t + -3.2t + -0.24t2 + 0.24t2 Combine like terms: 3.2t + -3.2t = 0.0 3 + -3.2t + 0.24t2 = 0.0 + -0.24t2 + 0.24t2 3 + -3.2t + 0.24t2 = -0.24t2 + 0.24t2 Combine like terms: -0.24t2 + 0.24t2 = 0.00 3 + -3.2t + 0.24t2 = 0.00 Begin completing the square. Divide all terms by 0.24 the coefficient of the squared term: Divide each side by '0.24'. 12.5 + -13.33333333t + t2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -13.33333333t + -12.5 + t2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -13.33333333t + t2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -13.33333333t + t2 = 0 + -12.5 -13.33333333t + t2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -13.33333333t + t2 = -12.5 The t term is -13.33333333t. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333t + 44.44444442 + t2 = -12.5 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333t + t2 = -12.5 + 44.44444442 Combine like terms: -12.5 + 44.44444442 = 31.94444442 44.44444442 + -13.33333333t + t2 = 31.94444442 Factor a perfect square on the left side: (t + -6.666666665)(t + -6.666666665) = 31.94444442 Calculate the square root of the right side: 5.65194165 Break this problem into two subproblems by setting (t + -6.666666665) equal to 5.65194165 and -5.65194165.Subproblem 1
t + -6.666666665 = 5.65194165 Simplifying t + -6.666666665 = 5.65194165 Reorder the terms: -6.666666665 + t = 5.65194165 Solving -6.666666665 + t = 5.65194165 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + t = 5.65194165 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + t = 5.65194165 + 6.666666665 t = 5.65194165 + 6.666666665 Combine like terms: 5.65194165 + 6.666666665 = 12.318608315 t = 12.318608315 Simplifying t = 12.318608315Subproblem 2
t + -6.666666665 = -5.65194165 Simplifying t + -6.666666665 = -5.65194165 Reorder the terms: -6.666666665 + t = -5.65194165 Solving -6.666666665 + t = -5.65194165 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + t = -5.65194165 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + t = -5.65194165 + 6.666666665 t = -5.65194165 + 6.666666665 Combine like terms: -5.65194165 + 6.666666665 = 1.014725015 t = 1.014725015 Simplifying t = 1.014725015Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.318608315, 1.014725015}
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