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Simplifying 13x2 + 200x + -2500 = 0 Reorder the terms: -2500 + 200x + 13x2 = 0 Solving -2500 + 200x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -192.3076923 + 15.38461538x + x2 = 0 Move the constant term to the right: Add '192.3076923' to each side of the equation. -192.3076923 + 15.38461538x + 192.3076923 + x2 = 0 + 192.3076923 Reorder the terms: -192.3076923 + 192.3076923 + 15.38461538x + x2 = 0 + 192.3076923 Combine like terms: -192.3076923 + 192.3076923 = 0.0000000 0.0000000 + 15.38461538x + x2 = 0 + 192.3076923 15.38461538x + x2 = 0 + 192.3076923 Combine like terms: 0 + 192.3076923 = 192.3076923 15.38461538x + x2 = 192.3076923 The x term is 15.38461538x. Take half its coefficient (7.69230769). Square it (59.17159760) and add it to both sides. Add '59.17159760' to each side of the equation. 15.38461538x + 59.17159760 + x2 = 192.3076923 + 59.17159760 Reorder the terms: 59.17159760 + 15.38461538x + x2 = 192.3076923 + 59.17159760 Combine like terms: 192.3076923 + 59.17159760 = 251.4792899 59.17159760 + 15.38461538x + x2 = 251.4792899 Factor a perfect square on the left side: (x + 7.69230769)(x + 7.69230769) = 251.4792899 Calculate the square root of the right side: 15.858098559 Break this problem into two subproblems by setting (x + 7.69230769) equal to 15.858098559 and -15.858098559.Subproblem 1
x + 7.69230769 = 15.858098559 Simplifying x + 7.69230769 = 15.858098559 Reorder the terms: 7.69230769 + x = 15.858098559 Solving 7.69230769 + x = 15.858098559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.69230769' to each side of the equation. 7.69230769 + -7.69230769 + x = 15.858098559 + -7.69230769 Combine like terms: 7.69230769 + -7.69230769 = 0.00000000 0.00000000 + x = 15.858098559 + -7.69230769 x = 15.858098559 + -7.69230769 Combine like terms: 15.858098559 + -7.69230769 = 8.165790869 x = 8.165790869 Simplifying x = 8.165790869Subproblem 2
x + 7.69230769 = -15.858098559 Simplifying x + 7.69230769 = -15.858098559 Reorder the terms: 7.69230769 + x = -15.858098559 Solving 7.69230769 + x = -15.858098559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.69230769' to each side of the equation. 7.69230769 + -7.69230769 + x = -15.858098559 + -7.69230769 Combine like terms: 7.69230769 + -7.69230769 = 0.00000000 0.00000000 + x = -15.858098559 + -7.69230769 x = -15.858098559 + -7.69230769 Combine like terms: -15.858098559 + -7.69230769 = -23.550406249 x = -23.550406249 Simplifying x = -23.550406249Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.165790869, -23.550406249}
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