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Simplifying 0 = -2.3t2 + 30t + 6 Reorder the terms: 0 = 6 + 30t + -2.3t2 Solving 0 = 6 + 30t + -2.3t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -30t + 2.3t2 = 6 + 30t + -2.3t2 + -6 + -30t + 2.3t2 Reorder the terms: -6 + -30t + 2.3t2 = 6 + -6 + 30t + -30t + -2.3t2 + 2.3t2 Combine like terms: 6 + -6 = 0 -6 + -30t + 2.3t2 = 0 + 30t + -30t + -2.3t2 + 2.3t2 -6 + -30t + 2.3t2 = 30t + -30t + -2.3t2 + 2.3t2 Combine like terms: 30t + -30t = 0 -6 + -30t + 2.3t2 = 0 + -2.3t2 + 2.3t2 -6 + -30t + 2.3t2 = -2.3t2 + 2.3t2 Combine like terms: -2.3t2 + 2.3t2 = 0.0 -6 + -30t + 2.3t2 = 0.0 Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -2.608695652 + -13.04347826t + t2 = 0 Move the constant term to the right: Add '2.608695652' to each side of the equation. -2.608695652 + -13.04347826t + 2.608695652 + t2 = 0 + 2.608695652 Reorder the terms: -2.608695652 + 2.608695652 + -13.04347826t + t2 = 0 + 2.608695652 Combine like terms: -2.608695652 + 2.608695652 = 0.000000000 0.000000000 + -13.04347826t + t2 = 0 + 2.608695652 -13.04347826t + t2 = 0 + 2.608695652 Combine like terms: 0 + 2.608695652 = 2.608695652 -13.04347826t + t2 = 2.608695652 The t term is -13.04347826t. Take half its coefficient (-6.52173913). Square it (42.53308128) and add it to both sides. Add '42.53308128' to each side of the equation. -13.04347826t + 42.53308128 + t2 = 2.608695652 + 42.53308128 Reorder the terms: 42.53308128 + -13.04347826t + t2 = 2.608695652 + 42.53308128 Combine like terms: 2.608695652 + 42.53308128 = 45.141776932 42.53308128 + -13.04347826t + t2 = 45.141776932 Factor a perfect square on the left side: (t + -6.52173913)(t + -6.52173913) = 45.141776932 Calculate the square root of the right side: 6.718763051 Break this problem into two subproblems by setting (t + -6.52173913) equal to 6.718763051 and -6.718763051.Subproblem 1
t + -6.52173913 = 6.718763051 Simplifying t + -6.52173913 = 6.718763051 Reorder the terms: -6.52173913 + t = 6.718763051 Solving -6.52173913 + t = 6.718763051 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.52173913' to each side of the equation. -6.52173913 + 6.52173913 + t = 6.718763051 + 6.52173913 Combine like terms: -6.52173913 + 6.52173913 = 0.00000000 0.00000000 + t = 6.718763051 + 6.52173913 t = 6.718763051 + 6.52173913 Combine like terms: 6.718763051 + 6.52173913 = 13.240502181 t = 13.240502181 Simplifying t = 13.240502181Subproblem 2
t + -6.52173913 = -6.718763051 Simplifying t + -6.52173913 = -6.718763051 Reorder the terms: -6.52173913 + t = -6.718763051 Solving -6.52173913 + t = -6.718763051 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.52173913' to each side of the equation. -6.52173913 + 6.52173913 + t = -6.718763051 + 6.52173913 Combine like terms: -6.52173913 + 6.52173913 = 0.00000000 0.00000000 + t = -6.718763051 + 6.52173913 t = -6.718763051 + 6.52173913 Combine like terms: -6.718763051 + 6.52173913 = -0.197023921 t = -0.197023921 Simplifying t = -0.197023921Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.240502181, -0.197023921}
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