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Simplifying 0 = 3.6t2 + -134t + -750 Reorder the terms: 0 = -750 + -134t + 3.6t2 Solving 0 = -750 + -134t + 3.6t2 Solving for variable 't'. Combine like terms: 0 + 750 = 750 750 + 134t + -3.6t2 = -750 + -134t + 3.6t2 + 750 + 134t + -3.6t2 Reorder the terms: 750 + 134t + -3.6t2 = -750 + 750 + -134t + 134t + 3.6t2 + -3.6t2 Combine like terms: -750 + 750 = 0 750 + 134t + -3.6t2 = 0 + -134t + 134t + 3.6t2 + -3.6t2 750 + 134t + -3.6t2 = -134t + 134t + 3.6t2 + -3.6t2 Combine like terms: -134t + 134t = 0 750 + 134t + -3.6t2 = 0 + 3.6t2 + -3.6t2 750 + 134t + -3.6t2 = 3.6t2 + -3.6t2 Combine like terms: 3.6t2 + -3.6t2 = 0.0 750 + 134t + -3.6t2 = 0.0 Begin completing the square. Divide all terms by -3.6 the coefficient of the squared term: Divide each side by '-3.6'. -208.3333333 + -37.22222222t + t2 = 0 Move the constant term to the right: Add '208.3333333' to each side of the equation. -208.3333333 + -37.22222222t + 208.3333333 + t2 = 0 + 208.3333333 Reorder the terms: -208.3333333 + 208.3333333 + -37.22222222t + t2 = 0 + 208.3333333 Combine like terms: -208.3333333 + 208.3333333 = 0.0000000 0.0000000 + -37.22222222t + t2 = 0 + 208.3333333 -37.22222222t + t2 = 0 + 208.3333333 Combine like terms: 0 + 208.3333333 = 208.3333333 -37.22222222t + t2 = 208.3333333 The t term is -37.22222222t. Take half its coefficient (-18.61111111). Square it (346.3734567) and add it to both sides. Add '346.3734567' to each side of the equation. -37.22222222t + 346.3734567 + t2 = 208.3333333 + 346.3734567 Reorder the terms: 346.3734567 + -37.22222222t + t2 = 208.3333333 + 346.3734567 Combine like terms: 208.3333333 + 346.3734567 = 554.70679 346.3734567 + -37.22222222t + t2 = 554.70679 Factor a perfect square on the left side: (t + -18.61111111)(t + -18.61111111) = 554.70679 Calculate the square root of the right side: 23.552214121 Break this problem into two subproblems by setting (t + -18.61111111) equal to 23.552214121 and -23.552214121.Subproblem 1
t + -18.61111111 = 23.552214121 Simplifying t + -18.61111111 = 23.552214121 Reorder the terms: -18.61111111 + t = 23.552214121 Solving -18.61111111 + t = 23.552214121 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.61111111' to each side of the equation. -18.61111111 + 18.61111111 + t = 23.552214121 + 18.61111111 Combine like terms: -18.61111111 + 18.61111111 = 0.00000000 0.00000000 + t = 23.552214121 + 18.61111111 t = 23.552214121 + 18.61111111 Combine like terms: 23.552214121 + 18.61111111 = 42.163325231 t = 42.163325231 Simplifying t = 42.163325231Subproblem 2
t + -18.61111111 = -23.552214121 Simplifying t + -18.61111111 = -23.552214121 Reorder the terms: -18.61111111 + t = -23.552214121 Solving -18.61111111 + t = -23.552214121 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.61111111' to each side of the equation. -18.61111111 + 18.61111111 + t = -23.552214121 + 18.61111111 Combine like terms: -18.61111111 + 18.61111111 = 0.00000000 0.00000000 + t = -23.552214121 + 18.61111111 t = -23.552214121 + 18.61111111 Combine like terms: -23.552214121 + 18.61111111 = -4.941103011 t = -4.941103011 Simplifying t = -4.941103011Solution
The solution to the problem is based on the solutions from the subproblems. t = {42.163325231, -4.941103011}
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