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Simplifying -1t2 + 30t + -100 = 0 Reorder the terms: -100 + 30t + -1t2 = 0 Solving -100 + 30t + -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 + -30t + t2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -30t + -100 + t2 = 0 + -100 Reorder the terms: 100 + -100 + -30t + t2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -30t + t2 = 0 + -100 -30t + t2 = 0 + -100 Combine like terms: 0 + -100 = -100 -30t + t2 = -100 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = -100 + 225 Reorder the terms: 225 + -30t + t2 = -100 + 225 Combine like terms: -100 + 225 = 125 225 + -30t + t2 = 125 Factor a perfect square on the left side: (t + -15)(t + -15) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (t + -15) equal to 11.180339887 and -11.180339887.Subproblem 1
t + -15 = 11.180339887 Simplifying t + -15 = 11.180339887 Reorder the terms: -15 + t = 11.180339887 Solving -15 + t = 11.180339887 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 11.180339887 + 15 Combine like terms: -15 + 15 = 0 0 + t = 11.180339887 + 15 t = 11.180339887 + 15 Combine like terms: 11.180339887 + 15 = 26.180339887 t = 26.180339887 Simplifying t = 26.180339887Subproblem 2
t + -15 = -11.180339887 Simplifying t + -15 = -11.180339887 Reorder the terms: -15 + t = -11.180339887 Solving -15 + t = -11.180339887 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -11.180339887 + 15 Combine like terms: -15 + 15 = 0 0 + t = -11.180339887 + 15 t = -11.180339887 + 15 Combine like terms: -11.180339887 + 15 = 3.819660113 t = 3.819660113 Simplifying t = 3.819660113Solution
The solution to the problem is based on the solutions from the subproblems. t = {26.180339887, 3.819660113}
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