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Simplifying 44 = 16t2 + 60t + -2 Reorder the terms: 44 = -2 + 60t + 16t2 Solving 44 = -2 + 60t + 16t2 Solving for variable 't'. Combine like terms: 44 + 2 = 46 46 + -60t + -16t2 = -2 + 60t + 16t2 + 2 + -60t + -16t2 Reorder the terms: 46 + -60t + -16t2 = -2 + 2 + 60t + -60t + 16t2 + -16t2 Combine like terms: -2 + 2 = 0 46 + -60t + -16t2 = 0 + 60t + -60t + 16t2 + -16t2 46 + -60t + -16t2 = 60t + -60t + 16t2 + -16t2 Combine like terms: 60t + -60t = 0 46 + -60t + -16t2 = 0 + 16t2 + -16t2 46 + -60t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 46 + -60t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(23 + -30t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + -30t + -8t2)' equal to zero and attempt to solve: Simplifying 23 + -30t + -8t2 = 0 Solving 23 + -30t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.875 + 3.75t + t2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + 3.75t + 2.875 + t2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + 3.75t + t2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + 3.75t + t2 = 0 + 2.875 3.75t + t2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 3.75t + t2 = 2.875 The t term is 3.75t. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75t + 3.515625 + t2 = 2.875 + 3.515625 Reorder the terms: 3.515625 + 3.75t + t2 = 2.875 + 3.515625 Combine like terms: 2.875 + 3.515625 = 6.390625 3.515625 + 3.75t + t2 = 6.390625 Factor a perfect square on the left side: (t + 1.875)(t + 1.875) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (t + 1.875) equal to 2.527968552 and -2.527968552.Subproblem 1
t + 1.875 = 2.527968552 Simplifying t + 1.875 = 2.527968552 Reorder the terms: 1.875 + t = 2.527968552 Solving 1.875 + t = 2.527968552 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = 2.527968552 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = 2.527968552 + -1.875 t = 2.527968552 + -1.875 Combine like terms: 2.527968552 + -1.875 = 0.652968552 t = 0.652968552 Simplifying t = 0.652968552Subproblem 2
t + 1.875 = -2.527968552 Simplifying t + 1.875 = -2.527968552 Reorder the terms: 1.875 + t = -2.527968552 Solving 1.875 + t = -2.527968552 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = -2.527968552 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = -2.527968552 + -1.875 t = -2.527968552 + -1.875 Combine like terms: -2.527968552 + -1.875 = -4.402968552 t = -4.402968552 Simplifying t = -4.402968552Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.652968552, -4.402968552}Solution
t = {0.652968552, -4.402968552}
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