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Simplifying 6.9t + 15 = -4.9t2 + 26t Reorder the terms: 15 + 6.9t = -4.9t2 + 26t Reorder the terms: 15 + 6.9t = 26t + -4.9t2 Solving 15 + 6.9t = 26t + -4.9t2 Solving for variable 't'. Combine like terms: 6.9t + -26t = -19.1t 15 + -19.1t + 4.9t2 = 26t + -4.9t2 + -26t + 4.9t2 Reorder the terms: 15 + -19.1t + 4.9t2 = 26t + -26t + -4.9t2 + 4.9t2 Combine like terms: 26t + -26t = 0 15 + -19.1t + 4.9t2 = 0 + -4.9t2 + 4.9t2 15 + -19.1t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 15 + -19.1t + 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'. 3.06122449 + -3.897959184t + t2 = 0 Move the constant term to the right: Add '-3.06122449' to each side of the equation. 3.06122449 + -3.897959184t + -3.06122449 + t2 = 0 + -3.06122449 Reorder the terms: 3.06122449 + -3.06122449 + -3.897959184t + t2 = 0 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + -3.897959184t + t2 = 0 + -3.06122449 -3.897959184t + t2 = 0 + -3.06122449 Combine like terms: 0 + -3.06122449 = -3.06122449 -3.897959184t + t2 = -3.06122449 The t term is -3.897959184t. Take half its coefficient (-1.948979592). Square it (3.798521450) and add it to both sides. Add '3.798521450' to each side of the equation. -3.897959184t + 3.798521450 + t2 = -3.06122449 + 3.798521450 Reorder the terms: 3.798521450 + -3.897959184t + t2 = -3.06122449 + 3.798521450 Combine like terms: -3.06122449 + 3.798521450 = 0.73729696 3.798521450 + -3.897959184t + t2 = 0.73729696 Factor a perfect square on the left side: (t + -1.948979592)(t + -1.948979592) = 0.73729696 Calculate the square root of the right side: 0.858659979 Break this problem into two subproblems by setting (t + -1.948979592) equal to 0.858659979 and -0.858659979.Subproblem 1
t + -1.948979592 = 0.858659979 Simplifying t + -1.948979592 = 0.858659979 Reorder the terms: -1.948979592 + t = 0.858659979 Solving -1.948979592 + t = 0.858659979 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.948979592' to each side of the equation. -1.948979592 + 1.948979592 + t = 0.858659979 + 1.948979592 Combine like terms: -1.948979592 + 1.948979592 = 0.000000000 0.000000000 + t = 0.858659979 + 1.948979592 t = 0.858659979 + 1.948979592 Combine like terms: 0.858659979 + 1.948979592 = 2.807639571 t = 2.807639571 Simplifying t = 2.807639571Subproblem 2
t + -1.948979592 = -0.858659979 Simplifying t + -1.948979592 = -0.858659979 Reorder the terms: -1.948979592 + t = -0.858659979 Solving -1.948979592 + t = -0.858659979 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.948979592' to each side of the equation. -1.948979592 + 1.948979592 + t = -0.858659979 + 1.948979592 Combine like terms: -1.948979592 + 1.948979592 = 0.000000000 0.000000000 + t = -0.858659979 + 1.948979592 t = -0.858659979 + 1.948979592 Combine like terms: -0.858659979 + 1.948979592 = 1.090319613 t = 1.090319613 Simplifying t = 1.090319613Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.807639571, 1.090319613}
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