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Simplifying -0.17t2 + 5t + -17 = 0 Reorder the terms: -17 + 5t + -0.17t2 = 0 Solving -17 + 5t + -0.17t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.17 the coefficient of the squared term: Divide each side by '-0.17'. 100 + -29.41176471t + t2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -29.41176471t + -100 + t2 = 0 + -100 Reorder the terms: 100 + -100 + -29.41176471t + t2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -29.41176471t + t2 = 0 + -100 -29.41176471t + t2 = 0 + -100 Combine like terms: 0 + -100 = -100 -29.41176471t + t2 = -100 The t term is -29.41176471t. Take half its coefficient (-14.70588236). Square it (216.2629760) and add it to both sides. Add '216.2629760' to each side of the equation. -29.41176471t + 216.2629760 + t2 = -100 + 216.2629760 Reorder the terms: 216.2629760 + -29.41176471t + t2 = -100 + 216.2629760 Combine like terms: -100 + 216.2629760 = 116.262976 216.2629760 + -29.41176471t + t2 = 116.262976 Factor a perfect square on the left side: (t + -14.70588236)(t + -14.70588236) = 116.262976 Calculate the square root of the right side: 10.782531057 Break this problem into two subproblems by setting (t + -14.70588236) equal to 10.782531057 and -10.782531057.Subproblem 1
t + -14.70588236 = 10.782531057 Simplifying t + -14.70588236 = 10.782531057 Reorder the terms: -14.70588236 + t = 10.782531057 Solving -14.70588236 + t = 10.782531057 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14.70588236' to each side of the equation. -14.70588236 + 14.70588236 + t = 10.782531057 + 14.70588236 Combine like terms: -14.70588236 + 14.70588236 = 0.00000000 0.00000000 + t = 10.782531057 + 14.70588236 t = 10.782531057 + 14.70588236 Combine like terms: 10.782531057 + 14.70588236 = 25.488413417 t = 25.488413417 Simplifying t = 25.488413417Subproblem 2
t + -14.70588236 = -10.782531057 Simplifying t + -14.70588236 = -10.782531057 Reorder the terms: -14.70588236 + t = -10.782531057 Solving -14.70588236 + t = -10.782531057 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14.70588236' to each side of the equation. -14.70588236 + 14.70588236 + t = -10.782531057 + 14.70588236 Combine like terms: -14.70588236 + 14.70588236 = 0.00000000 0.00000000 + t = -10.782531057 + 14.70588236 t = -10.782531057 + 14.70588236 Combine like terms: -10.782531057 + 14.70588236 = 3.923351303 t = 3.923351303 Simplifying t = 3.923351303Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.488413417, 3.923351303}
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