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Simplifying 30 = -4.9t2 + 27t + 2.4 Reorder the terms: 30 = 2.4 + 27t + -4.9t2 Solving 30 = 2.4 + 27t + -4.9t2 Solving for variable 't'. Combine like terms: 30 + -2.4 = 27.6 27.6 + -27t + 4.9t2 = 2.4 + 27t + -4.9t2 + -2.4 + -27t + 4.9t2 Reorder the terms: 27.6 + -27t + 4.9t2 = 2.4 + -2.4 + 27t + -27t + -4.9t2 + 4.9t2 Combine like terms: 2.4 + -2.4 = 0.0 27.6 + -27t + 4.9t2 = 0.0 + 27t + -27t + -4.9t2 + 4.9t2 27.6 + -27t + 4.9t2 = 27t + -27t + -4.9t2 + 4.9t2 Combine like terms: 27t + -27t = 0 27.6 + -27t + 4.9t2 = 0 + -4.9t2 + 4.9t2 27.6 + -27t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 27.6 + -27t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 5.632653061 + -5.510204082t + t2 = 0 Move the constant term to the right: Add '-5.632653061' to each side of the equation. 5.632653061 + -5.510204082t + -5.632653061 + t2 = 0 + -5.632653061 Reorder the terms: 5.632653061 + -5.632653061 + -5.510204082t + t2 = 0 + -5.632653061 Combine like terms: 5.632653061 + -5.632653061 = 0.000000000 0.000000000 + -5.510204082t + t2 = 0 + -5.632653061 -5.510204082t + t2 = 0 + -5.632653061 Combine like terms: 0 + -5.632653061 = -5.632653061 -5.510204082t + t2 = -5.632653061 The t term is -5.510204082t. Take half its coefficient (-2.755102041). Square it (7.590587256) and add it to both sides. Add '7.590587256' to each side of the equation. -5.510204082t + 7.590587256 + t2 = -5.632653061 + 7.590587256 Reorder the terms: 7.590587256 + -5.510204082t + t2 = -5.632653061 + 7.590587256 Combine like terms: -5.632653061 + 7.590587256 = 1.957934195 7.590587256 + -5.510204082t + t2 = 1.957934195 Factor a perfect square on the left side: (t + -2.755102041)(t + -2.755102041) = 1.957934195 Calculate the square root of the right side: 1.399262018 Break this problem into two subproblems by setting (t + -2.755102041) equal to 1.399262018 and -1.399262018.Subproblem 1
t + -2.755102041 = 1.399262018 Simplifying t + -2.755102041 = 1.399262018 Reorder the terms: -2.755102041 + t = 1.399262018 Solving -2.755102041 + t = 1.399262018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.755102041' to each side of the equation. -2.755102041 + 2.755102041 + t = 1.399262018 + 2.755102041 Combine like terms: -2.755102041 + 2.755102041 = 0.000000000 0.000000000 + t = 1.399262018 + 2.755102041 t = 1.399262018 + 2.755102041 Combine like terms: 1.399262018 + 2.755102041 = 4.154364059 t = 4.154364059 Simplifying t = 4.154364059Subproblem 2
t + -2.755102041 = -1.399262018 Simplifying t + -2.755102041 = -1.399262018 Reorder the terms: -2.755102041 + t = -1.399262018 Solving -2.755102041 + t = -1.399262018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.755102041' to each side of the equation. -2.755102041 + 2.755102041 + t = -1.399262018 + 2.755102041 Combine like terms: -2.755102041 + 2.755102041 = 0.000000000 0.000000000 + t = -1.399262018 + 2.755102041 t = -1.399262018 + 2.755102041 Combine like terms: -1.399262018 + 2.755102041 = 1.355840023 t = 1.355840023 Simplifying t = 1.355840023Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.154364059, 1.355840023}
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