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Simplifying -7(t + -4)(-1t + 2) = 11 Reorder the terms: -7(-4 + t)(-1t + 2) = 11 Reorder the terms: -7(-4 + t)(2 + -1t) = 11 Multiply (-4 + t) * (2 + -1t) -7(-4(2 + -1t) + t(2 + -1t)) = 11 -7((2 * -4 + -1t * -4) + t(2 + -1t)) = 11 -7((-8 + 4t) + t(2 + -1t)) = 11 -7(-8 + 4t + (2 * t + -1t * t)) = 11 -7(-8 + 4t + (2t + -1t2)) = 11 Combine like terms: 4t + 2t = 6t -7(-8 + 6t + -1t2) = 11 (-8 * -7 + 6t * -7 + -1t2 * -7) = 11 (56 + -42t + 7t2) = 11 Solving 56 + -42t + 7t2 = 11 Solving for variable 't'. Reorder the terms: 56 + -11 + -42t + 7t2 = 11 + -11 Combine like terms: 56 + -11 = 45 45 + -42t + 7t2 = 11 + -11 Combine like terms: 11 + -11 = 0 45 + -42t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 6.428571429 + -6t + t2 = 0 Move the constant term to the right: Add '-6.428571429' to each side of the equation. 6.428571429 + -6t + -6.428571429 + t2 = 0 + -6.428571429 Reorder the terms: 6.428571429 + -6.428571429 + -6t + t2 = 0 + -6.428571429 Combine like terms: 6.428571429 + -6.428571429 = 0.000000000 0.000000000 + -6t + t2 = 0 + -6.428571429 -6t + t2 = 0 + -6.428571429 Combine like terms: 0 + -6.428571429 = -6.428571429 -6t + t2 = -6.428571429 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -6.428571429 + 9 Reorder the terms: 9 + -6t + t2 = -6.428571429 + 9 Combine like terms: -6.428571429 + 9 = 2.571428571 9 + -6t + t2 = 2.571428571 Factor a perfect square on the left side: (t + -3)(t + -3) = 2.571428571 Calculate the square root of the right side: 1.603567451 Break this problem into two subproblems by setting (t + -3) equal to 1.603567451 and -1.603567451.Subproblem 1
t + -3 = 1.603567451 Simplifying t + -3 = 1.603567451 Reorder the terms: -3 + t = 1.603567451 Solving -3 + t = 1.603567451 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 1.603567451 + 3 Combine like terms: -3 + 3 = 0 0 + t = 1.603567451 + 3 t = 1.603567451 + 3 Combine like terms: 1.603567451 + 3 = 4.603567451 t = 4.603567451 Simplifying t = 4.603567451Subproblem 2
t + -3 = -1.603567451 Simplifying t + -3 = -1.603567451 Reorder the terms: -3 + t = -1.603567451 Solving -3 + t = -1.603567451 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -1.603567451 + 3 Combine like terms: -3 + 3 = 0 0 + t = -1.603567451 + 3 t = -1.603567451 + 3 Combine like terms: -1.603567451 + 3 = 1.396432549 t = 1.396432549 Simplifying t = 1.396432549Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.603567451, 1.396432549}
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