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Simplifying 6 = -16t2 + 50t + 100 Reorder the terms: 6 = 100 + 50t + -16t2 Solving 6 = 100 + 50t + -16t2 Solving for variable 't'. Combine like terms: 6 + -100 = -94 -94 + -50t + 16t2 = 100 + 50t + -16t2 + -100 + -50t + 16t2 Reorder the terms: -94 + -50t + 16t2 = 100 + -100 + 50t + -50t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -94 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2 -94 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 -94 + -50t + 16t2 = 0 + -16t2 + 16t2 -94 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -94 + -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + -25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + -25t + 8t2)' equal to zero and attempt to solve: Simplifying -47 + -25t + 8t2 = 0 Solving -47 + -25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.875 + -3.125t + t2 = 0 Move the constant term to the right: Add '5.875' to each side of the equation. -5.875 + -3.125t + 5.875 + t2 = 0 + 5.875 Reorder the terms: -5.875 + 5.875 + -3.125t + t2 = 0 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + -3.125t + t2 = 0 + 5.875 -3.125t + t2 = 0 + 5.875 Combine like terms: 0 + 5.875 = 5.875 -3.125t + t2 = 5.875 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = 5.875 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 5.875 + 2.44140625 Combine like terms: 5.875 + 2.44140625 = 8.31640625 2.44140625 + -3.125t + t2 = 8.31640625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 8.31640625 Calculate the square root of the right side: 2.883817999 Break this problem into two subproblems by setting (t + -1.5625) equal to 2.883817999 and -2.883817999.Subproblem 1
t + -1.5625 = 2.883817999 Simplifying t + -1.5625 = 2.883817999 Reorder the terms: -1.5625 + t = 2.883817999 Solving -1.5625 + t = 2.883817999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 2.883817999 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 2.883817999 + 1.5625 t = 2.883817999 + 1.5625 Combine like terms: 2.883817999 + 1.5625 = 4.446317999 t = 4.446317999 Simplifying t = 4.446317999Subproblem 2
t + -1.5625 = -2.883817999 Simplifying t + -1.5625 = -2.883817999 Reorder the terms: -1.5625 + t = -2.883817999 Solving -1.5625 + t = -2.883817999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -2.883817999 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -2.883817999 + 1.5625 t = -2.883817999 + 1.5625 Combine like terms: -2.883817999 + 1.5625 = -1.321317999 t = -1.321317999 Simplifying t = -1.321317999Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.446317999, -1.321317999}Solution
t = {4.446317999, -1.321317999}
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