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Simplifying 80 = t2 + -100t Reorder the terms: 80 = -100t + t2 Solving 80 = -100t + t2 Solving for variable 't'. Reorder the terms: 80 + 100t + -1t2 = -100t + 100t + t2 + -1t2 Combine like terms: -100t + 100t = 0 80 + 100t + -1t2 = 0 + t2 + -1t2 80 + 100t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 80 + 100t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + -100t + t2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -100t + 80 + t2 = 0 + 80 Reorder the terms: -80 + 80 + -100t + t2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -100t + t2 = 0 + 80 -100t + t2 = 0 + 80 Combine like terms: 0 + 80 = 80 -100t + t2 = 80 The t term is -100t. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100t + 2500 + t2 = 80 + 2500 Reorder the terms: 2500 + -100t + t2 = 80 + 2500 Combine like terms: 80 + 2500 = 2580 2500 + -100t + t2 = 2580 Factor a perfect square on the left side: (t + -50)(t + -50) = 2580 Calculate the square root of the right side: 50.793700397 Break this problem into two subproblems by setting (t + -50) equal to 50.793700397 and -50.793700397.Subproblem 1
t + -50 = 50.793700397 Simplifying t + -50 = 50.793700397 Reorder the terms: -50 + t = 50.793700397 Solving -50 + t = 50.793700397 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + t = 50.793700397 + 50 Combine like terms: -50 + 50 = 0 0 + t = 50.793700397 + 50 t = 50.793700397 + 50 Combine like terms: 50.793700397 + 50 = 100.793700397 t = 100.793700397 Simplifying t = 100.793700397Subproblem 2
t + -50 = -50.793700397 Simplifying t + -50 = -50.793700397 Reorder the terms: -50 + t = -50.793700397 Solving -50 + t = -50.793700397 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + t = -50.793700397 + 50 Combine like terms: -50 + 50 = 0 0 + t = -50.793700397 + 50 t = -50.793700397 + 50 Combine like terms: -50.793700397 + 50 = -0.793700397 t = -0.793700397 Simplifying t = -0.793700397Solution
The solution to the problem is based on the solutions from the subproblems. t = {100.793700397, -0.793700397}
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