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Simplifying 200t + -2t2 + -500 = 0 Reorder the terms: -500 + 200t + -2t2 = 0 Solving -500 + 200t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-250 + 100t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-250 + 100t + -1t2)' equal to zero and attempt to solve: Simplifying -250 + 100t + -1t2 = 0 Solving -250 + 100t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 250 + -100t + t2 = 0 Move the constant term to the right: Add '-250' to each side of the equation. 250 + -100t + -250 + t2 = 0 + -250 Reorder the terms: 250 + -250 + -100t + t2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -100t + t2 = 0 + -250 -100t + t2 = 0 + -250 Combine like terms: 0 + -250 = -250 -100t + t2 = -250 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 = -250 + 2500 Reorder the terms: 2500 + -100t + t2 = -250 + 2500 Combine like terms: -250 + 2500 = 2250 2500 + -100t + t2 = 2250 Factor a perfect square on the left side: (t + -50)(t + -50) = 2250 Calculate the square root of the right side: 47.434164903 Break this problem into two subproblems by setting (t + -50) equal to 47.434164903 and -47.434164903.Subproblem 1
t + -50 = 47.434164903 Simplifying t + -50 = 47.434164903 Reorder the terms: -50 + t = 47.434164903 Solving -50 + t = 47.434164903 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 = 47.434164903 + 50 Combine like terms: -50 + 50 = 0 0 + t = 47.434164903 + 50 t = 47.434164903 + 50 Combine like terms: 47.434164903 + 50 = 97.434164903 t = 97.434164903 Simplifying t = 97.434164903Subproblem 2
t + -50 = -47.434164903 Simplifying t + -50 = -47.434164903 Reorder the terms: -50 + t = -47.434164903 Solving -50 + t = -47.434164903 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 = -47.434164903 + 50 Combine like terms: -50 + 50 = 0 0 + t = -47.434164903 + 50 t = -47.434164903 + 50 Combine like terms: -47.434164903 + 50 = 2.565835097 t = 2.565835097 Simplifying t = 2.565835097Solution
The solution to the problem is based on the solutions from the subproblems. t = {97.434164903, 2.565835097}Solution
t = {97.434164903, 2.565835097}
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