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Simplifying 11t(4 + -1t) = 2(5 + -3t) (4 * 11t + -1t * 11t) = 2(5 + -3t) (44t + -11t2) = 2(5 + -3t) 44t + -11t2 = (5 * 2 + -3t * 2) 44t + -11t2 = (10 + -6t) Solving 44t + -11t2 = 10 + -6t Solving for variable 't'. Reorder the terms: -10 + 44t + 6t + -11t2 = 10 + -6t + -10 + 6t Combine like terms: 44t + 6t = 50t -10 + 50t + -11t2 = 10 + -6t + -10 + 6t Reorder the terms: -10 + 50t + -11t2 = 10 + -10 + -6t + 6t Combine like terms: 10 + -10 = 0 -10 + 50t + -11t2 = 0 + -6t + 6t -10 + 50t + -11t2 = -6t + 6t Combine like terms: -6t + 6t = 0 -10 + 50t + -11t2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. 0.9090909091 + -4.545454545t + t2 = 0 Move the constant term to the right: Add '-0.9090909091' to each side of the equation. 0.9090909091 + -4.545454545t + -0.9090909091 + t2 = 0 + -0.9090909091 Reorder the terms: 0.9090909091 + -0.9090909091 + -4.545454545t + t2 = 0 + -0.9090909091 Combine like terms: 0.9090909091 + -0.9090909091 = 0.0000000000 0.0000000000 + -4.545454545t + t2 = 0 + -0.9090909091 -4.545454545t + t2 = 0 + -0.9090909091 Combine like terms: 0 + -0.9090909091 = -0.9090909091 -4.545454545t + t2 = -0.9090909091 The t term is -4.545454545t. Take half its coefficient (-2.272727273). Square it (5.165289257) and add it to both sides. Add '5.165289257' to each side of the equation. -4.545454545t + 5.165289257 + t2 = -0.9090909091 + 5.165289257 Reorder the terms: 5.165289257 + -4.545454545t + t2 = -0.9090909091 + 5.165289257 Combine like terms: -0.9090909091 + 5.165289257 = 4.2561983479 5.165289257 + -4.545454545t + t2 = 4.2561983479 Factor a perfect square on the left side: (t + -2.272727273)(t + -2.272727273) = 4.2561983479 Calculate the square root of the right side: 2.063055585 Break this problem into two subproblems by setting (t + -2.272727273) equal to 2.063055585 and -2.063055585.Subproblem 1
t + -2.272727273 = 2.063055585 Simplifying t + -2.272727273 = 2.063055585 Reorder the terms: -2.272727273 + t = 2.063055585 Solving -2.272727273 + t = 2.063055585 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.272727273' to each side of the equation. -2.272727273 + 2.272727273 + t = 2.063055585 + 2.272727273 Combine like terms: -2.272727273 + 2.272727273 = 0.000000000 0.000000000 + t = 2.063055585 + 2.272727273 t = 2.063055585 + 2.272727273 Combine like terms: 2.063055585 + 2.272727273 = 4.335782858 t = 4.335782858 Simplifying t = 4.335782858Subproblem 2
t + -2.272727273 = -2.063055585 Simplifying t + -2.272727273 = -2.063055585 Reorder the terms: -2.272727273 + t = -2.063055585 Solving -2.272727273 + t = -2.063055585 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.272727273' to each side of the equation. -2.272727273 + 2.272727273 + t = -2.063055585 + 2.272727273 Combine like terms: -2.272727273 + 2.272727273 = 0.000000000 0.000000000 + t = -2.063055585 + 2.272727273 t = -2.063055585 + 2.272727273 Combine like terms: -2.063055585 + 2.272727273 = 0.209671688 t = 0.209671688 Simplifying t = 0.209671688Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.335782858, 0.209671688}
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