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Simplifying -1t2 + 20t + 100 = 0 Reorder the terms: 100 + 20t + -1t2 = 0 Solving 100 + 20t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + -20t + t2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -20t + 100 + t2 = 0 + 100 Reorder the terms: -100 + 100 + -20t + t2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -20t + t2 = 0 + 100 -20t + t2 = 0 + 100 Combine like terms: 0 + 100 = 100 -20t + t2 = 100 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 100 + 100 Reorder the terms: 100 + -20t + t2 = 100 + 100 Combine like terms: 100 + 100 = 200 100 + -20t + t2 = 200 Factor a perfect square on the left side: (t + -10)(t + -10) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (t + -10) equal to 14.142135624 and -14.142135624.Subproblem 1
t + -10 = 14.142135624 Simplifying t + -10 = 14.142135624 Reorder the terms: -10 + t = 14.142135624 Solving -10 + t = 14.142135624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 14.142135624 + 10 Combine like terms: -10 + 10 = 0 0 + t = 14.142135624 + 10 t = 14.142135624 + 10 Combine like terms: 14.142135624 + 10 = 24.142135624 t = 24.142135624 Simplifying t = 24.142135624Subproblem 2
t + -10 = -14.142135624 Simplifying t + -10 = -14.142135624 Reorder the terms: -10 + t = -14.142135624 Solving -10 + t = -14.142135624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -14.142135624 + 10 Combine like terms: -10 + 10 = 0 0 + t = -14.142135624 + 10 t = -14.142135624 + 10 Combine like terms: -14.142135624 + 10 = -4.142135624 t = -4.142135624 Simplifying t = -4.142135624Solution
The solution to the problem is based on the solutions from the subproblems. t = {24.142135624, -4.142135624}
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