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Simplifying 162 + 17t + -1.1t2 = 0 Solving 162 + 17t + -1.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1.1 the coefficient of the squared term: Divide each side by '-1.1'. -147.2727273 + -15.45454545t + t2 = 0 Move the constant term to the right: Add '147.2727273' to each side of the equation. -147.2727273 + -15.45454545t + 147.2727273 + t2 = 0 + 147.2727273 Reorder the terms: -147.2727273 + 147.2727273 + -15.45454545t + t2 = 0 + 147.2727273 Combine like terms: -147.2727273 + 147.2727273 = 0.0000000 0.0000000 + -15.45454545t + t2 = 0 + 147.2727273 -15.45454545t + t2 = 0 + 147.2727273 Combine like terms: 0 + 147.2727273 = 147.2727273 -15.45454545t + t2 = 147.2727273 The t term is -15.45454545t. Take half its coefficient (-7.727272725). Square it (59.71074377) and add it to both sides. Add '59.71074377' to each side of the equation. -15.45454545t + 59.71074377 + t2 = 147.2727273 + 59.71074377 Reorder the terms: 59.71074377 + -15.45454545t + t2 = 147.2727273 + 59.71074377 Combine like terms: 147.2727273 + 59.71074377 = 206.98347107 59.71074377 + -15.45454545t + t2 = 206.98347107 Factor a perfect square on the left side: (t + -7.727272725)(t + -7.727272725) = 206.98347107 Calculate the square root of the right side: 14.386920138 Break this problem into two subproblems by setting (t + -7.727272725) equal to 14.386920138 and -14.386920138.Subproblem 1
t + -7.727272725 = 14.386920138 Simplifying t + -7.727272725 = 14.386920138 Reorder the terms: -7.727272725 + t = 14.386920138 Solving -7.727272725 + t = 14.386920138 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.727272725' to each side of the equation. -7.727272725 + 7.727272725 + t = 14.386920138 + 7.727272725 Combine like terms: -7.727272725 + 7.727272725 = 0.000000000 0.000000000 + t = 14.386920138 + 7.727272725 t = 14.386920138 + 7.727272725 Combine like terms: 14.386920138 + 7.727272725 = 22.114192863 t = 22.114192863 Simplifying t = 22.114192863Subproblem 2
t + -7.727272725 = -14.386920138 Simplifying t + -7.727272725 = -14.386920138 Reorder the terms: -7.727272725 + t = -14.386920138 Solving -7.727272725 + t = -14.386920138 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.727272725' to each side of the equation. -7.727272725 + 7.727272725 + t = -14.386920138 + 7.727272725 Combine like terms: -7.727272725 + 7.727272725 = 0.000000000 0.000000000 + t = -14.386920138 + 7.727272725 t = -14.386920138 + 7.727272725 Combine like terms: -14.386920138 + 7.727272725 = -6.659647413 t = -6.659647413 Simplifying t = -6.659647413Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.114192863, -6.659647413}
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