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Simplifying 200(t) = -4t2 + 776 Reorder the terms: 200t = 776 + -4t2 Solving 200t = 776 + -4t2 Solving for variable 't'. Reorder the terms: -776 + 200t + 4t2 = 776 + -4t2 + -776 + 4t2 Reorder the terms: -776 + 200t + 4t2 = 776 + -776 + -4t2 + 4t2 Combine like terms: 776 + -776 = 0 -776 + 200t + 4t2 = 0 + -4t2 + 4t2 -776 + 200t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 -776 + 200t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-194 + 50t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-194 + 50t + t2)' equal to zero and attempt to solve: Simplifying -194 + 50t + t2 = 0 Solving -194 + 50t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '194' to each side of the equation. -194 + 50t + 194 + t2 = 0 + 194 Reorder the terms: -194 + 194 + 50t + t2 = 0 + 194 Combine like terms: -194 + 194 = 0 0 + 50t + t2 = 0 + 194 50t + t2 = 0 + 194 Combine like terms: 0 + 194 = 194 50t + t2 = 194 The t term is 50t. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50t + 625 + t2 = 194 + 625 Reorder the terms: 625 + 50t + t2 = 194 + 625 Combine like terms: 194 + 625 = 819 625 + 50t + t2 = 819 Factor a perfect square on the left side: (t + 25)(t + 25) = 819 Calculate the square root of the right side: 28.618176043 Break this problem into two subproblems by setting (t + 25) equal to 28.618176043 and -28.618176043.Subproblem 1
t + 25 = 28.618176043 Simplifying t + 25 = 28.618176043 Reorder the terms: 25 + t = 28.618176043 Solving 25 + t = 28.618176043 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = 28.618176043 + -25 Combine like terms: 25 + -25 = 0 0 + t = 28.618176043 + -25 t = 28.618176043 + -25 Combine like terms: 28.618176043 + -25 = 3.618176043 t = 3.618176043 Simplifying t = 3.618176043Subproblem 2
t + 25 = -28.618176043 Simplifying t + 25 = -28.618176043 Reorder the terms: 25 + t = -28.618176043 Solving 25 + t = -28.618176043 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = -28.618176043 + -25 Combine like terms: 25 + -25 = 0 0 + t = -28.618176043 + -25 t = -28.618176043 + -25 Combine like terms: -28.618176043 + -25 = -53.618176043 t = -53.618176043 Simplifying t = -53.618176043Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.618176043, -53.618176043}Solution
t = {3.618176043, -53.618176043}
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