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Simplifying 4.9t2 + 5t = 650 Reorder the terms: 5t + 4.9t2 = 650 Solving 5t + 4.9t2 = 650 Solving for variable 't'. Reorder the terms: -650 + 5t + 4.9t2 = 650 + -650 Combine like terms: 650 + -650 = 0 -650 + 5t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -132.6530612 + 1.020408163t + t2 = 0 Move the constant term to the right: Add '132.6530612' to each side of the equation. -132.6530612 + 1.020408163t + 132.6530612 + t2 = 0 + 132.6530612 Reorder the terms: -132.6530612 + 132.6530612 + 1.020408163t + t2 = 0 + 132.6530612 Combine like terms: -132.6530612 + 132.6530612 = 0.0000000 0.0000000 + 1.020408163t + t2 = 0 + 132.6530612 1.020408163t + t2 = 0 + 132.6530612 Combine like terms: 0 + 132.6530612 = 132.6530612 1.020408163t + t2 = 132.6530612 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 = 132.6530612 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163t + t2 = 132.6530612 + 0.2603082048 Combine like terms: 132.6530612 + 0.2603082048 = 132.9133694048 0.2603082048 + 1.020408163t + t2 = 132.9133694048 Factor a perfect square on the left side: (t + 0.5102040815)(t + 0.5102040815) = 132.9133694048 Calculate the square root of the right side: 11.52880607 Break this problem into two subproblems by setting (t + 0.5102040815) equal to 11.52880607 and -11.52880607.Subproblem 1
t + 0.5102040815 = 11.52880607 Simplifying t + 0.5102040815 = 11.52880607 Reorder the terms: 0.5102040815 + t = 11.52880607 Solving 0.5102040815 + t = 11.52880607 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 = 11.52880607 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = 11.52880607 + -0.5102040815 t = 11.52880607 + -0.5102040815 Combine like terms: 11.52880607 + -0.5102040815 = 11.0186019885 t = 11.0186019885 Simplifying t = 11.0186019885Subproblem 2
t + 0.5102040815 = -11.52880607 Simplifying t + 0.5102040815 = -11.52880607 Reorder the terms: 0.5102040815 + t = -11.52880607 Solving 0.5102040815 + t = -11.52880607 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 = -11.52880607 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = -11.52880607 + -0.5102040815 t = -11.52880607 + -0.5102040815 Combine like terms: -11.52880607 + -0.5102040815 = -12.0390101515 t = -12.0390101515 Simplifying t = -12.0390101515Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.0186019885, -12.0390101515}
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