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Simplifying t2 + -200t + 2500 = 0 Reorder the terms: 2500 + -200t + t2 = 0 Solving 2500 + -200t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -200t + -2500 + t2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -200t + t2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -200t + t2 = 0 + -2500 -200t + t2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -200t + t2 = -2500 The t term is -200t. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200t + 10000 + t2 = -2500 + 10000 Reorder the terms: 10000 + -200t + t2 = -2500 + 10000 Combine like terms: -2500 + 10000 = 7500 10000 + -200t + t2 = 7500 Factor a perfect square on the left side: (t + -100)(t + -100) = 7500 Calculate the square root of the right side: 86.602540378 Break this problem into two subproblems by setting (t + -100) equal to 86.602540378 and -86.602540378.Subproblem 1
t + -100 = 86.602540378 Simplifying t + -100 = 86.602540378 Reorder the terms: -100 + t = 86.602540378 Solving -100 + t = 86.602540378 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + t = 86.602540378 + 100 Combine like terms: -100 + 100 = 0 0 + t = 86.602540378 + 100 t = 86.602540378 + 100 Combine like terms: 86.602540378 + 100 = 186.602540378 t = 186.602540378 Simplifying t = 186.602540378Subproblem 2
t + -100 = -86.602540378 Simplifying t + -100 = -86.602540378 Reorder the terms: -100 + t = -86.602540378 Solving -100 + t = -86.602540378 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + t = -86.602540378 + 100 Combine like terms: -100 + 100 = 0 0 + t = -86.602540378 + 100 t = -86.602540378 + 100 Combine like terms: -86.602540378 + 100 = 13.397459622 t = 13.397459622 Simplifying t = 13.397459622Solution
The solution to the problem is based on the solutions from the subproblems. t = {186.602540378, 13.397459622}
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