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Simplifying 5t2 + -200t + 1000 = 0 Reorder the terms: 1000 + -200t + 5t2 = 0 Solving 1000 + -200t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(200 + -40t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(200 + -40t + t2)' equal to zero and attempt to solve: Simplifying 200 + -40t + t2 = 0 Solving 200 + -40t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -40t + -200 + t2 = 0 + -200 Reorder the terms: 200 + -200 + -40t + t2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -40t + t2 = 0 + -200 -40t + t2 = 0 + -200 Combine like terms: 0 + -200 = -200 -40t + t2 = -200 The t term is -40t. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40t + 400 + t2 = -200 + 400 Reorder the terms: 400 + -40t + t2 = -200 + 400 Combine like terms: -200 + 400 = 200 400 + -40t + t2 = 200 Factor a perfect square on the left side: (t + -20)(t + -20) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (t + -20) equal to 14.142135624 and -14.142135624.Subproblem 1
t + -20 = 14.142135624 Simplifying t + -20 = 14.142135624 Reorder the terms: -20 + t = 14.142135624 Solving -20 + t = 14.142135624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 14.142135624 + 20 Combine like terms: -20 + 20 = 0 0 + t = 14.142135624 + 20 t = 14.142135624 + 20 Combine like terms: 14.142135624 + 20 = 34.142135624 t = 34.142135624 Simplifying t = 34.142135624Subproblem 2
t + -20 = -14.142135624 Simplifying t + -20 = -14.142135624 Reorder the terms: -20 + t = -14.142135624 Solving -20 + t = -14.142135624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -14.142135624 + 20 Combine like terms: -20 + 20 = 0 0 + t = -14.142135624 + 20 t = -14.142135624 + 20 Combine like terms: -14.142135624 + 20 = 5.857864376 t = 5.857864376 Simplifying t = 5.857864376Solution
The solution to the problem is based on the solutions from the subproblems. t = {34.142135624, 5.857864376}Solution
t = {34.142135624, 5.857864376}
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