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Simplifying 0.00014x2 + 0.00323x + -1.13 = 0 Reorder the terms: -1.13 + 0.00323x + 0.00014x2 = 0 Solving -1.13 + 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'. -8071.428571 + 23.07142857x + x2 = 0 Move the constant term to the right: Add '8071.428571' to each side of the equation. -8071.428571 + 23.07142857x + 8071.428571 + x2 = 0 + 8071.428571 Reorder the terms: -8071.428571 + 8071.428571 + 23.07142857x + x2 = 0 + 8071.428571 Combine like terms: -8071.428571 + 8071.428571 = 0.000000 0.000000 + 23.07142857x + x2 = 0 + 8071.428571 23.07142857x + x2 = 0 + 8071.428571 Combine like terms: 0 + 8071.428571 = 8071.428571 23.07142857x + x2 = 8071.428571 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 = 8071.428571 + 133.0727042 Reorder the terms: 133.0727042 + 23.07142857x + x2 = 8071.428571 + 133.0727042 Combine like terms: 8071.428571 + 133.0727042 = 8204.5012752 133.0727042 + 23.07142857x + x2 = 8204.5012752 Factor a perfect square on the left side: (x + 11.53571429)(x + 11.53571429) = 8204.5012752 Calculate the square root of the right side: 90.578702106 Break this problem into two subproblems by setting (x + 11.53571429) equal to 90.578702106 and -90.578702106.Subproblem 1
x + 11.53571429 = 90.578702106 Simplifying x + 11.53571429 = 90.578702106 Reorder the terms: 11.53571429 + x = 90.578702106 Solving 11.53571429 + x = 90.578702106 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 = 90.578702106 + -11.53571429 Combine like terms: 11.53571429 + -11.53571429 = 0.00000000 0.00000000 + x = 90.578702106 + -11.53571429 x = 90.578702106 + -11.53571429 Combine like terms: 90.578702106 + -11.53571429 = 79.042987816 x = 79.042987816 Simplifying x = 79.042987816Subproblem 2
x + 11.53571429 = -90.578702106 Simplifying x + 11.53571429 = -90.578702106 Reorder the terms: 11.53571429 + x = -90.578702106 Solving 11.53571429 + x = -90.578702106 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 = -90.578702106 + -11.53571429 Combine like terms: 11.53571429 + -11.53571429 = 0.00000000 0.00000000 + x = -90.578702106 + -11.53571429 x = -90.578702106 + -11.53571429 Combine like terms: -90.578702106 + -11.53571429 = -102.114416396 x = -102.114416396 Simplifying x = -102.114416396Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.042987816, -102.114416396}
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