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Simplifying 16t2 + -62t + 58 = 0 Reorder the terms: 58 + -62t + 16t2 = 0 Solving 58 + -62t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(29 + -31t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + -31t + 8t2)' equal to zero and attempt to solve: Simplifying 29 + -31t + 8t2 = 0 Solving 29 + -31t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.625 + -3.875t + t2 = 0 Move the constant term to the right: Add '-3.625' to each side of the equation. 3.625 + -3.875t + -3.625 + t2 = 0 + -3.625 Reorder the terms: 3.625 + -3.625 + -3.875t + t2 = 0 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + -3.875t + t2 = 0 + -3.625 -3.875t + t2 = 0 + -3.625 Combine like terms: 0 + -3.625 = -3.625 -3.875t + t2 = -3.625 The t term is -3.875t. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875t + 3.75390625 + t2 = -3.625 + 3.75390625 Reorder the terms: 3.75390625 + -3.875t + t2 = -3.625 + 3.75390625 Combine like terms: -3.625 + 3.75390625 = 0.12890625 3.75390625 + -3.875t + t2 = 0.12890625 Factor a perfect square on the left side: (t + -1.9375)(t + -1.9375) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (t + -1.9375) equal to 0.359035165 and -0.359035165.Subproblem 1
t + -1.9375 = 0.359035165 Simplifying t + -1.9375 = 0.359035165 Reorder the terms: -1.9375 + t = 0.359035165 Solving -1.9375 + t = 0.359035165 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = 0.359035165 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = 0.359035165 + 1.9375 t = 0.359035165 + 1.9375 Combine like terms: 0.359035165 + 1.9375 = 2.296535165 t = 2.296535165 Simplifying t = 2.296535165Subproblem 2
t + -1.9375 = -0.359035165 Simplifying t + -1.9375 = -0.359035165 Reorder the terms: -1.9375 + t = -0.359035165 Solving -1.9375 + t = -0.359035165 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = -0.359035165 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = -0.359035165 + 1.9375 t = -0.359035165 + 1.9375 Combine like terms: -0.359035165 + 1.9375 = 1.578464835 t = 1.578464835 Simplifying t = 1.578464835Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.296535165, 1.578464835}Solution
t = {2.296535165, 1.578464835}
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