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Simplifying 50t = -16t2 + 63t + 4 Reorder the terms: 50t = 4 + 63t + -16t2 Solving 50t = 4 + 63t + -16t2 Solving for variable 't'. Reorder the terms: -4 + 50t + -63t + 16t2 = 4 + 63t + -16t2 + -4 + -63t + 16t2 Combine like terms: 50t + -63t = -13t -4 + -13t + 16t2 = 4 + 63t + -16t2 + -4 + -63t + 16t2 Reorder the terms: -4 + -13t + 16t2 = 4 + -4 + 63t + -63t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -13t + 16t2 = 0 + 63t + -63t + -16t2 + 16t2 -4 + -13t + 16t2 = 63t + -63t + -16t2 + 16t2 Combine like terms: 63t + -63t = 0 -4 + -13t + 16t2 = 0 + -16t2 + 16t2 -4 + -13t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -13t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -0.8125t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.8125t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.8125t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.8125t + t2 = 0 + 0.25 -0.8125t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.8125t + t2 = 0.25 The t term is -0.8125t. Take half its coefficient (-0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. -0.8125t + 0.1650390625 + t2 = 0.25 + 0.1650390625 Reorder the terms: 0.1650390625 + -0.8125t + t2 = 0.25 + 0.1650390625 Combine like terms: 0.25 + 0.1650390625 = 0.4150390625 0.1650390625 + -0.8125t + t2 = 0.4150390625 Factor a perfect square on the left side: (t + -0.40625)(t + -0.40625) = 0.4150390625 Calculate the square root of the right side: 0.644235254 Break this problem into two subproblems by setting (t + -0.40625) equal to 0.644235254 and -0.644235254.Subproblem 1
t + -0.40625 = 0.644235254 Simplifying t + -0.40625 = 0.644235254 Reorder the terms: -0.40625 + t = 0.644235254 Solving -0.40625 + t = 0.644235254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + t = 0.644235254 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + t = 0.644235254 + 0.40625 t = 0.644235254 + 0.40625 Combine like terms: 0.644235254 + 0.40625 = 1.050485254 t = 1.050485254 Simplifying t = 1.050485254Subproblem 2
t + -0.40625 = -0.644235254 Simplifying t + -0.40625 = -0.644235254 Reorder the terms: -0.40625 + t = -0.644235254 Solving -0.40625 + t = -0.644235254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.40625' to each side of the equation. -0.40625 + 0.40625 + t = -0.644235254 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + t = -0.644235254 + 0.40625 t = -0.644235254 + 0.40625 Combine like terms: -0.644235254 + 0.40625 = -0.237985254 t = -0.237985254 Simplifying t = -0.237985254Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.050485254, -0.237985254}
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