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Simplifying 0.00014x2 + 0.00323x + -1.3 = 0 Reorder the terms: -1.3 + 0.00323x + 0.00014x2 = 0 Solving -1.3 + 0.00323x + 0.00014x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.00014 the coefficient of the squared term: Divide each side by '0.00014'. -9285.714286 + 23.07142857x + x2 = 0 Move the constant term to the right: Add '9285.714286' to each side of the equation. -9285.714286 + 23.07142857x + 9285.714286 + x2 = 0 + 9285.714286 Reorder the terms: -9285.714286 + 9285.714286 + 23.07142857x + x2 = 0 + 9285.714286 Combine like terms: -9285.714286 + 9285.714286 = 0.000000 0.000000 + 23.07142857x + x2 = 0 + 9285.714286 23.07142857x + x2 = 0 + 9285.714286 Combine like terms: 0 + 9285.714286 = 9285.714286 23.07142857x + x2 = 9285.714286 The x term is 23.07142857x. Take half its coefficient (11.53571429). Square it (133.0727042) and add it to both sides. Add '133.0727042' to each side of the equation. 23.07142857x + 133.0727042 + x2 = 9285.714286 + 133.0727042 Reorder the terms: 133.0727042 + 23.07142857x + x2 = 9285.714286 + 133.0727042 Combine like terms: 9285.714286 + 133.0727042 = 9418.7869902 133.0727042 + 23.07142857x + x2 = 9418.7869902 Factor a perfect square on the left side: (x + 11.53571429)(x + 11.53571429) = 9418.7869902 Calculate the square root of the right side: 97.050435291 Break this problem into two subproblems by setting (x + 11.53571429) equal to 97.050435291 and -97.050435291.Subproblem 1
x + 11.53571429 = 97.050435291 Simplifying x + 11.53571429 = 97.050435291 Reorder the terms: 11.53571429 + x = 97.050435291 Solving 11.53571429 + x = 97.050435291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.53571429' to each side of the equation. 11.53571429 + -11.53571429 + x = 97.050435291 + -11.53571429 Combine like terms: 11.53571429 + -11.53571429 = 0.00000000 0.00000000 + x = 97.050435291 + -11.53571429 x = 97.050435291 + -11.53571429 Combine like terms: 97.050435291 + -11.53571429 = 85.514721001 x = 85.514721001 Simplifying x = 85.514721001Subproblem 2
x + 11.53571429 = -97.050435291 Simplifying x + 11.53571429 = -97.050435291 Reorder the terms: 11.53571429 + x = -97.050435291 Solving 11.53571429 + x = -97.050435291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.53571429' to each side of the equation. 11.53571429 + -11.53571429 + x = -97.050435291 + -11.53571429 Combine like terms: 11.53571429 + -11.53571429 = 0.00000000 0.00000000 + x = -97.050435291 + -11.53571429 x = -97.050435291 + -11.53571429 Combine like terms: -97.050435291 + -11.53571429 = -108.586149581 x = -108.586149581 Simplifying x = -108.586149581Solution
The solution to the problem is based on the solutions from the subproblems. x = {85.514721001, -108.586149581}
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