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Simplifying 14t + -1.86t2 = 14 Solving 14t + -1.86t2 = 14 Solving for variable 't'. Reorder the terms: -14 + 14t + -1.86t2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 14t + -1.86t2 = 0 Begin completing the square. Divide all terms by -1.86 the coefficient of the squared term: Divide each side by '-1.86'. 7.52688172 + -7.52688172t + t2 = 0 Move the constant term to the right: Add '-7.52688172' to each side of the equation. 7.52688172 + -7.52688172t + -7.52688172 + t2 = 0 + -7.52688172 Reorder the terms: 7.52688172 + -7.52688172 + -7.52688172t + t2 = 0 + -7.52688172 Combine like terms: 7.52688172 + -7.52688172 = 0.00000000 0.00000000 + -7.52688172t + t2 = 0 + -7.52688172 -7.52688172t + t2 = 0 + -7.52688172 Combine like terms: 0 + -7.52688172 = -7.52688172 -7.52688172t + t2 = -7.52688172 The t term is -7.52688172t. Take half its coefficient (-3.76344086). Square it (14.16348711) and add it to both sides. Add '14.16348711' to each side of the equation. -7.52688172t + 14.16348711 + t2 = -7.52688172 + 14.16348711 Reorder the terms: 14.16348711 + -7.52688172t + t2 = -7.52688172 + 14.16348711 Combine like terms: -7.52688172 + 14.16348711 = 6.63660539 14.16348711 + -7.52688172t + t2 = 6.63660539 Factor a perfect square on the left side: (t + -3.76344086)(t + -3.76344086) = 6.63660539 Calculate the square root of the right side: 2.576160979 Break this problem into two subproblems by setting (t + -3.76344086) equal to 2.576160979 and -2.576160979.Subproblem 1
t + -3.76344086 = 2.576160979 Simplifying t + -3.76344086 = 2.576160979 Reorder the terms: -3.76344086 + t = 2.576160979 Solving -3.76344086 + t = 2.576160979 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.76344086' to each side of the equation. -3.76344086 + 3.76344086 + t = 2.576160979 + 3.76344086 Combine like terms: -3.76344086 + 3.76344086 = 0.00000000 0.00000000 + t = 2.576160979 + 3.76344086 t = 2.576160979 + 3.76344086 Combine like terms: 2.576160979 + 3.76344086 = 6.339601839 t = 6.339601839 Simplifying t = 6.339601839Subproblem 2
t + -3.76344086 = -2.576160979 Simplifying t + -3.76344086 = -2.576160979 Reorder the terms: -3.76344086 + t = -2.576160979 Solving -3.76344086 + t = -2.576160979 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.76344086' to each side of the equation. -3.76344086 + 3.76344086 + t = -2.576160979 + 3.76344086 Combine like terms: -3.76344086 + 3.76344086 = 0.00000000 0.00000000 + t = -2.576160979 + 3.76344086 t = -2.576160979 + 3.76344086 Combine like terms: -2.576160979 + 3.76344086 = 1.187279881 t = 1.187279881 Simplifying t = 1.187279881Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.339601839, 1.187279881}
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