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Simplifying -2500x2 + 65000x + -170000 = 13 Reorder the terms: -170000 + 65000x + -2500x2 = 13 Solving -170000 + 65000x + -2500x2 = 13 Solving for variable 'x'. Reorder the terms: -170000 + -13 + 65000x + -2500x2 = 13 + -13 Combine like terms: -170000 + -13 = -170013 -170013 + 65000x + -2500x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -170013 + 65000x + -2500x2 = 0 Begin completing the square. Divide all terms by -2500 the coefficient of the squared term: Divide each side by '-2500'. 68.0052 + -26x + x2 = 0 Move the constant term to the right: Add '-68.0052' to each side of the equation. 68.0052 + -26x + -68.0052 + x2 = 0 + -68.0052 Reorder the terms: 68.0052 + -68.0052 + -26x + x2 = 0 + -68.0052 Combine like terms: 68.0052 + -68.0052 = 0.0000 0.0000 + -26x + x2 = 0 + -68.0052 -26x + x2 = 0 + -68.0052 Combine like terms: 0 + -68.0052 = -68.0052 -26x + x2 = -68.0052 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -68.0052 + 169 Reorder the terms: 169 + -26x + x2 = -68.0052 + 169 Combine like terms: -68.0052 + 169 = 100.9948 169 + -26x + x2 = 100.9948 Factor a perfect square on the left side: (x + -13)(x + -13) = 100.9948 Calculate the square root of the right side: 10.049616908 Break this problem into two subproblems by setting (x + -13) equal to 10.049616908 and -10.049616908.Subproblem 1
x + -13 = 10.049616908 Simplifying x + -13 = 10.049616908 Reorder the terms: -13 + x = 10.049616908 Solving -13 + x = 10.049616908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 10.049616908 + 13 Combine like terms: -13 + 13 = 0 0 + x = 10.049616908 + 13 x = 10.049616908 + 13 Combine like terms: 10.049616908 + 13 = 23.049616908 x = 23.049616908 Simplifying x = 23.049616908Subproblem 2
x + -13 = -10.049616908 Simplifying x + -13 = -10.049616908 Reorder the terms: -13 + x = -10.049616908 Solving -13 + x = -10.049616908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -10.049616908 + 13 Combine like terms: -13 + 13 = 0 0 + x = -10.049616908 + 13 x = -10.049616908 + 13 Combine like terms: -10.049616908 + 13 = 2.950383092 x = 2.950383092 Simplifying x = 2.950383092Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.049616908, 2.950383092}
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