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Simplifying -4.6t2 + 8t + 11 = 0 Reorder the terms: 11 + 8t + -4.6t2 = 0 Solving 11 + 8t + -4.6t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.6 the coefficient of the squared term: Divide each side by '-4.6'. -2.391304348 + -1.739130435t + t2 = 0 Move the constant term to the right: Add '2.391304348' to each side of the equation. -2.391304348 + -1.739130435t + 2.391304348 + t2 = 0 + 2.391304348 Reorder the terms: -2.391304348 + 2.391304348 + -1.739130435t + t2 = 0 + 2.391304348 Combine like terms: -2.391304348 + 2.391304348 = 0.000000000 0.000000000 + -1.739130435t + t2 = 0 + 2.391304348 -1.739130435t + t2 = 0 + 2.391304348 Combine like terms: 0 + 2.391304348 = 2.391304348 -1.739130435t + t2 = 2.391304348 The t term is -1.739130435t. Take half its coefficient (-0.8695652175). Square it (0.7561436675) and add it to both sides. Add '0.7561436675' to each side of the equation. -1.739130435t + 0.7561436675 + t2 = 2.391304348 + 0.7561436675 Reorder the terms: 0.7561436675 + -1.739130435t + t2 = 2.391304348 + 0.7561436675 Combine like terms: 2.391304348 + 0.7561436675 = 3.1474480155 0.7561436675 + -1.739130435t + t2 = 3.1474480155 Factor a perfect square on the left side: (t + -0.8695652175)(t + -0.8695652175) = 3.1474480155 Calculate the square root of the right side: 1.774104849 Break this problem into two subproblems by setting (t + -0.8695652175) equal to 1.774104849 and -1.774104849.Subproblem 1
t + -0.8695652175 = 1.774104849 Simplifying t + -0.8695652175 = 1.774104849 Reorder the terms: -0.8695652175 + t = 1.774104849 Solving -0.8695652175 + t = 1.774104849 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8695652175' to each side of the equation. -0.8695652175 + 0.8695652175 + t = 1.774104849 + 0.8695652175 Combine like terms: -0.8695652175 + 0.8695652175 = 0.0000000000 0.0000000000 + t = 1.774104849 + 0.8695652175 t = 1.774104849 + 0.8695652175 Combine like terms: 1.774104849 + 0.8695652175 = 2.6436700665 t = 2.6436700665 Simplifying t = 2.6436700665Subproblem 2
t + -0.8695652175 = -1.774104849 Simplifying t + -0.8695652175 = -1.774104849 Reorder the terms: -0.8695652175 + t = -1.774104849 Solving -0.8695652175 + t = -1.774104849 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8695652175' to each side of the equation. -0.8695652175 + 0.8695652175 + t = -1.774104849 + 0.8695652175 Combine like terms: -0.8695652175 + 0.8695652175 = 0.0000000000 0.0000000000 + t = -1.774104849 + 0.8695652175 t = -1.774104849 + 0.8695652175 Combine like terms: -1.774104849 + 0.8695652175 = -0.9045396315 t = -0.9045396315 Simplifying t = -0.9045396315Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.6436700665, -0.9045396315}
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