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Simplifying 4.9t2 + -13.5t = 66 Reorder the terms: -13.5t + 4.9t2 = 66 Solving -13.5t + 4.9t2 = 66 Solving for variable 't'. Reorder the terms: -66 + -13.5t + 4.9t2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + -13.5t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -13.46938776 + -2.755102041t + t2 = 0 Move the constant term to the right: Add '13.46938776' to each side of the equation. -13.46938776 + -2.755102041t + 13.46938776 + t2 = 0 + 13.46938776 Reorder the terms: -13.46938776 + 13.46938776 + -2.755102041t + t2 = 0 + 13.46938776 Combine like terms: -13.46938776 + 13.46938776 = 0.00000000 0.00000000 + -2.755102041t + t2 = 0 + 13.46938776 -2.755102041t + t2 = 0 + 13.46938776 Combine like terms: 0 + 13.46938776 = 13.46938776 -2.755102041t + t2 = 13.46938776 The t term is -2.755102041t. Take half its coefficient (-1.377551021). Square it (1.897646815) and add it to both sides. Add '1.897646815' to each side of the equation. -2.755102041t + 1.897646815 + t2 = 13.46938776 + 1.897646815 Reorder the terms: 1.897646815 + -2.755102041t + t2 = 13.46938776 + 1.897646815 Combine like terms: 13.46938776 + 1.897646815 = 15.367034575 1.897646815 + -2.755102041t + t2 = 15.367034575 Factor a perfect square on the left side: (t + -1.377551021)(t + -1.377551021) = 15.367034575 Calculate the square root of the right side: 3.92008094 Break this problem into two subproblems by setting (t + -1.377551021) equal to 3.92008094 and -3.92008094.Subproblem 1
t + -1.377551021 = 3.92008094 Simplifying t + -1.377551021 = 3.92008094 Reorder the terms: -1.377551021 + t = 3.92008094 Solving -1.377551021 + t = 3.92008094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.377551021' to each side of the equation. -1.377551021 + 1.377551021 + t = 3.92008094 + 1.377551021 Combine like terms: -1.377551021 + 1.377551021 = 0.000000000 0.000000000 + t = 3.92008094 + 1.377551021 t = 3.92008094 + 1.377551021 Combine like terms: 3.92008094 + 1.377551021 = 5.297631961 t = 5.297631961 Simplifying t = 5.297631961Subproblem 2
t + -1.377551021 = -3.92008094 Simplifying t + -1.377551021 = -3.92008094 Reorder the terms: -1.377551021 + t = -3.92008094 Solving -1.377551021 + t = -3.92008094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.377551021' to each side of the equation. -1.377551021 + 1.377551021 + t = -3.92008094 + 1.377551021 Combine like terms: -1.377551021 + 1.377551021 = 0.000000000 0.000000000 + t = -3.92008094 + 1.377551021 t = -3.92008094 + 1.377551021 Combine like terms: -3.92008094 + 1.377551021 = -2.542529919 t = -2.542529919 Simplifying t = -2.542529919Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.297631961, -2.542529919}
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