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Simplifying t = (-2 + t)(t + -7) Reorder the terms: t = (-2 + t)(-7 + t) Multiply (-2 + t) * (-7 + t) t = (-2(-7 + t) + t(-7 + t)) t = ((-7 * -2 + t * -2) + t(-7 + t)) t = ((14 + -2t) + t(-7 + t)) t = (14 + -2t + (-7 * t + t * t)) t = (14 + -2t + (-7t + t2)) Combine like terms: -2t + -7t = -9t t = (14 + -9t + t2) Solving t = 14 + -9t + t2 Solving for variable 't'. Reorder the terms: -14 + t + 9t + -1t2 = 14 + -9t + t2 + -14 + 9t + -1t2 Combine like terms: t + 9t = 10t -14 + 10t + -1t2 = 14 + -9t + t2 + -14 + 9t + -1t2 Reorder the terms: -14 + 10t + -1t2 = 14 + -14 + -9t + 9t + t2 + -1t2 Combine like terms: 14 + -14 = 0 -14 + 10t + -1t2 = 0 + -9t + 9t + t2 + -1t2 -14 + 10t + -1t2 = -9t + 9t + t2 + -1t2 Combine like terms: -9t + 9t = 0 -14 + 10t + -1t2 = 0 + t2 + -1t2 -14 + 10t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 -14 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 14 + -10t + t2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -10t + -14 + t2 = 0 + -14 Reorder the terms: 14 + -14 + -10t + t2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -10t + t2 = 0 + -14 -10t + t2 = 0 + -14 Combine like terms: 0 + -14 = -14 -10t + t2 = -14 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -14 + 25 Reorder the terms: 25 + -10t + t2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + -10t + t2 = 11 Factor a perfect square on the left side: (t + -5)(t + -5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (t + -5) equal to 3.31662479 and -3.31662479.Subproblem 1
t + -5 = 3.31662479 Simplifying t + -5 = 3.31662479 Reorder the terms: -5 + t = 3.31662479 Solving -5 + t = 3.31662479 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + t = 3.31662479 + 5 t = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 t = 8.31662479 Simplifying t = 8.31662479Subproblem 2
t + -5 = -3.31662479 Simplifying t + -5 = -3.31662479 Reorder the terms: -5 + t = -3.31662479 Solving -5 + t = -3.31662479 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + t = -3.31662479 + 5 t = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 t = 1.68337521 Simplifying t = 1.68337521Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.31662479, 1.68337521}
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