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Simplifying 17t2 + -2000t + 40000 = 0 Reorder the terms: 40000 + -2000t + 17t2 = 0 Solving 40000 + -2000t + 17t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 2352.941176 + -117.6470588t + t2 = 0 Move the constant term to the right: Add '-2352.941176' to each side of the equation. 2352.941176 + -117.6470588t + -2352.941176 + t2 = 0 + -2352.941176 Reorder the terms: 2352.941176 + -2352.941176 + -117.6470588t + t2 = 0 + -2352.941176 Combine like terms: 2352.941176 + -2352.941176 = 0.000000 0.000000 + -117.6470588t + t2 = 0 + -2352.941176 -117.6470588t + t2 = 0 + -2352.941176 Combine like terms: 0 + -2352.941176 = -2352.941176 -117.6470588t + t2 = -2352.941176 The t term is -117.6470588t. Take half its coefficient (-58.8235294). Square it (3460.207611) and add it to both sides. Add '3460.207611' to each side of the equation. -117.6470588t + 3460.207611 + t2 = -2352.941176 + 3460.207611 Reorder the terms: 3460.207611 + -117.6470588t + t2 = -2352.941176 + 3460.207611 Combine like terms: -2352.941176 + 3460.207611 = 1107.266435 3460.207611 + -117.6470588t + t2 = 1107.266435 Factor a perfect square on the left side: (t + -58.8235294)(t + -58.8235294) = 1107.266435 Calculate the square root of the right side: 33.275613217 Break this problem into two subproblems by setting (t + -58.8235294) equal to 33.275613217 and -33.275613217.Subproblem 1
t + -58.8235294 = 33.275613217 Simplifying t + -58.8235294 = 33.275613217 Reorder the terms: -58.8235294 + t = 33.275613217 Solving -58.8235294 + t = 33.275613217 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '58.8235294' to each side of the equation. -58.8235294 + 58.8235294 + t = 33.275613217 + 58.8235294 Combine like terms: -58.8235294 + 58.8235294 = 0.0000000 0.0000000 + t = 33.275613217 + 58.8235294 t = 33.275613217 + 58.8235294 Combine like terms: 33.275613217 + 58.8235294 = 92.099142617 t = 92.099142617 Simplifying t = 92.099142617Subproblem 2
t + -58.8235294 = -33.275613217 Simplifying t + -58.8235294 = -33.275613217 Reorder the terms: -58.8235294 + t = -33.275613217 Solving -58.8235294 + t = -33.275613217 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '58.8235294' to each side of the equation. -58.8235294 + 58.8235294 + t = -33.275613217 + 58.8235294 Combine like terms: -58.8235294 + 58.8235294 = 0.0000000 0.0000000 + t = -33.275613217 + 58.8235294 t = -33.275613217 + 58.8235294 Combine like terms: -33.275613217 + 58.8235294 = 25.547916183 t = 25.547916183 Simplifying t = 25.547916183Solution
The solution to the problem is based on the solutions from the subproblems. t = {92.099142617, 25.547916183}
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