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Simplifying 0 = 50t2 + -550t + 600 Reorder the terms: 0 = 600 + -550t + 50t2 Solving 0 = 600 + -550t + 50t2 Solving for variable 't'. Combine like terms: 0 + -600 = -600 -600 + 550t + -50t2 = 600 + -550t + 50t2 + -600 + 550t + -50t2 Reorder the terms: -600 + 550t + -50t2 = 600 + -600 + -550t + 550t + 50t2 + -50t2 Combine like terms: 600 + -600 = 0 -600 + 550t + -50t2 = 0 + -550t + 550t + 50t2 + -50t2 -600 + 550t + -50t2 = -550t + 550t + 50t2 + -50t2 Combine like terms: -550t + 550t = 0 -600 + 550t + -50t2 = 0 + 50t2 + -50t2 -600 + 550t + -50t2 = 50t2 + -50t2 Combine like terms: 50t2 + -50t2 = 0 -600 + 550t + -50t2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-12 + 11t + -1t2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-12 + 11t + -1t2)' equal to zero and attempt to solve: Simplifying -12 + 11t + -1t2 = 0 Solving -12 + 11t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -11t + t2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -11t + -12 + t2 = 0 + -12 Reorder the terms: 12 + -12 + -11t + t2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -11t + t2 = 0 + -12 -11t + t2 = 0 + -12 Combine like terms: 0 + -12 = -12 -11t + t2 = -12 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = -12 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -12 + 30.25 Combine like terms: -12 + 30.25 = 18.25 30.25 + -11t + t2 = 18.25 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (t + -5.5) equal to 4.272001873 and -4.272001873.Subproblem 1
t + -5.5 = 4.272001873 Simplifying t + -5.5 = 4.272001873 Reorder the terms: -5.5 + t = 4.272001873 Solving -5.5 + t = 4.272001873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = 4.272001873 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 4.272001873 + 5.5 t = 4.272001873 + 5.5 Combine like terms: 4.272001873 + 5.5 = 9.772001873 t = 9.772001873 Simplifying t = 9.772001873Subproblem 2
t + -5.5 = -4.272001873 Simplifying t + -5.5 = -4.272001873 Reorder the terms: -5.5 + t = -4.272001873 Solving -5.5 + t = -4.272001873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = -4.272001873 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -4.272001873 + 5.5 t = -4.272001873 + 5.5 Combine like terms: -4.272001873 + 5.5 = 1.227998127 t = 1.227998127 Simplifying t = 1.227998127Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.772001873, 1.227998127}Solution
t = {9.772001873, 1.227998127}
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