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Simplifying 490t = 100 + t2 Solving 490t = 100 + t2 Solving for variable 't'. Reorder the terms: -100 + 490t + -1t2 = 100 + t2 + -100 + -1t2 Reorder the terms: -100 + 490t + -1t2 = 100 + -100 + t2 + -1t2 Combine like terms: 100 + -100 = 0 -100 + 490t + -1t2 = 0 + t2 + -1t2 -100 + 490t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 -100 + 490t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -490t + t2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -490t + -100 + t2 = 0 + -100 Reorder the terms: 100 + -100 + -490t + t2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -490t + t2 = 0 + -100 -490t + t2 = 0 + -100 Combine like terms: 0 + -100 = -100 -490t + t2 = -100 The t term is -490t. Take half its coefficient (-245). Square it (60025) and add it to both sides. Add '60025' to each side of the equation. -490t + 60025 + t2 = -100 + 60025 Reorder the terms: 60025 + -490t + t2 = -100 + 60025 Combine like terms: -100 + 60025 = 59925 60025 + -490t + t2 = 59925 Factor a perfect square on the left side: (t + -245)(t + -245) = 59925 Calculate the square root of the right side: 244.795833298 Break this problem into two subproblems by setting (t + -245) equal to 244.795833298 and -244.795833298.Subproblem 1
t + -245 = 244.795833298 Simplifying t + -245 = 244.795833298 Reorder the terms: -245 + t = 244.795833298 Solving -245 + t = 244.795833298 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '245' to each side of the equation. -245 + 245 + t = 244.795833298 + 245 Combine like terms: -245 + 245 = 0 0 + t = 244.795833298 + 245 t = 244.795833298 + 245 Combine like terms: 244.795833298 + 245 = 489.795833298 t = 489.795833298 Simplifying t = 489.795833298Subproblem 2
t + -245 = -244.795833298 Simplifying t + -245 = -244.795833298 Reorder the terms: -245 + t = -244.795833298 Solving -245 + t = -244.795833298 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '245' to each side of the equation. -245 + 245 + t = -244.795833298 + 245 Combine like terms: -245 + 245 = 0 0 + t = -244.795833298 + 245 t = -244.795833298 + 245 Combine like terms: -244.795833298 + 245 = 0.204166702 t = 0.204166702 Simplifying t = 0.204166702Solution
The solution to the problem is based on the solutions from the subproblems. t = {489.795833298, 0.204166702}
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