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Simplifying 26(t) = -16t2 + 32t + 26 Reorder the terms: 26t = 26 + 32t + -16t2 Solving 26t = 26 + 32t + -16t2 Solving for variable 't'. Reorder the terms: -26 + 26t + -32t + 16t2 = 26 + 32t + -16t2 + -26 + -32t + 16t2 Combine like terms: 26t + -32t = -6t -26 + -6t + 16t2 = 26 + 32t + -16t2 + -26 + -32t + 16t2 Reorder the terms: -26 + -6t + 16t2 = 26 + -26 + 32t + -32t + -16t2 + 16t2 Combine like terms: 26 + -26 = 0 -26 + -6t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -26 + -6t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -26 + -6t + 16t2 = 0 + -16t2 + 16t2 -26 + -6t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -26 + -6t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -3t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -3t + 8t2)' equal to zero and attempt to solve: Simplifying -13 + -3t + 8t2 = 0 Solving -13 + -3t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + -0.375t + t2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -0.375t + 1.625 + t2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -0.375t + t2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -0.375t + t2 = 0 + 1.625 -0.375t + t2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -0.375t + t2 = 1.625 The t term is -0.375t. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375t + 0.03515625 + t2 = 1.625 + 0.03515625 Reorder the terms: 0.03515625 + -0.375t + t2 = 1.625 + 0.03515625 Combine like terms: 1.625 + 0.03515625 = 1.66015625 0.03515625 + -0.375t + t2 = 1.66015625 Factor a perfect square on the left side: (t + -0.1875)(t + -0.1875) = 1.66015625 Calculate the square root of the right side: 1.288470508 Break this problem into two subproblems by setting (t + -0.1875) equal to 1.288470508 and -1.288470508.Subproblem 1
t + -0.1875 = 1.288470508 Simplifying t + -0.1875 = 1.288470508 Reorder the terms: -0.1875 + t = 1.288470508 Solving -0.1875 + t = 1.288470508 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + t = 1.288470508 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + t = 1.288470508 + 0.1875 t = 1.288470508 + 0.1875 Combine like terms: 1.288470508 + 0.1875 = 1.475970508 t = 1.475970508 Simplifying t = 1.475970508Subproblem 2
t + -0.1875 = -1.288470508 Simplifying t + -0.1875 = -1.288470508 Reorder the terms: -0.1875 + t = -1.288470508 Solving -0.1875 + t = -1.288470508 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + t = -1.288470508 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + t = -1.288470508 + 0.1875 t = -1.288470508 + 0.1875 Combine like terms: -1.288470508 + 0.1875 = -1.100970508 t = -1.100970508 Simplifying t = -1.100970508Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.475970508, -1.100970508}Solution
t = {1.475970508, -1.100970508}
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