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Simplifying -50 = (5 + -10) * t + (0 + -4.9) * t2 Combine like terms: 5 + -10 = -5 -50 = (-5) * t + (0 + -4.9) * t2 Combine like terms: 0 + -4.9 = -4.9 -50 = -5t + (-4.9) * t2 Solving -50 = -5t + -4.9t2 Solving for variable 't'. Reorder the terms: -50 + 5t + 4.9t2 = -5t + 5t + -4.9t2 + 4.9t2 Combine like terms: -5t + 5t = 0 -50 + 5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -50 + 5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -50 + 5t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -10.20408163 + 1.020408163t + t2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 1.020408163t + 10.20408163 + t2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 1.020408163t + t2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 1.020408163t + t2 = 0 + 10.20408163 1.020408163t + t2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 1.020408163t + t2 = 10.20408163 The t term is 1.020408163t. Take half its coefficient (0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. 1.020408163t + 0.2603082048 + t2 = 10.20408163 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163t + t2 = 10.20408163 + 0.2603082048 Combine like terms: 10.20408163 + 0.2603082048 = 10.4643898348 0.2603082048 + 1.020408163t + t2 = 10.4643898348 Factor a perfect square on the left side: (t + 0.5102040815)(t + 0.5102040815) = 10.4643898348 Calculate the square root of the right side: 3.234870915 Break this problem into two subproblems by setting (t + 0.5102040815) equal to 3.234870915 and -3.234870915.Subproblem 1
t + 0.5102040815 = 3.234870915 Simplifying t + 0.5102040815 = 3.234870915 Reorder the terms: 0.5102040815 + t = 3.234870915 Solving 0.5102040815 + t = 3.234870915 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + t = 3.234870915 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = 3.234870915 + -0.5102040815 t = 3.234870915 + -0.5102040815 Combine like terms: 3.234870915 + -0.5102040815 = 2.7246668335 t = 2.7246668335 Simplifying t = 2.7246668335Subproblem 2
t + 0.5102040815 = -3.234870915 Simplifying t + 0.5102040815 = -3.234870915 Reorder the terms: 0.5102040815 + t = -3.234870915 Solving 0.5102040815 + t = -3.234870915 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + t = -3.234870915 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = -3.234870915 + -0.5102040815 t = -3.234870915 + -0.5102040815 Combine like terms: -3.234870915 + -0.5102040815 = -3.7450749965 t = -3.7450749965 Simplifying t = -3.7450749965Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.7246668335, -3.7450749965}
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