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Simplifying 0.0014x2 + 0.00323x + -1.3 = 0 Reorder the terms: -1.3 + 0.00323x + 0.0014x2 = 0 Solving -1.3 + 0.00323x + 0.0014x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0014 the coefficient of the squared term: Divide each side by '0.0014'. -928.5714286 + 2.307142857x + x2 = 0 Move the constant term to the right: Add '928.5714286' to each side of the equation. -928.5714286 + 2.307142857x + 928.5714286 + x2 = 0 + 928.5714286 Reorder the terms: -928.5714286 + 928.5714286 + 2.307142857x + x2 = 0 + 928.5714286 Combine like terms: -928.5714286 + 928.5714286 = 0.0000000 0.0000000 + 2.307142857x + x2 = 0 + 928.5714286 2.307142857x + x2 = 0 + 928.5714286 Combine like terms: 0 + 928.5714286 = 928.5714286 2.307142857x + x2 = 928.5714286 The x term is 2.307142857x. Take half its coefficient (1.153571429). Square it (1.330727042) and add it to both sides. Add '1.330727042' to each side of the equation. 2.307142857x + 1.330727042 + x2 = 928.5714286 + 1.330727042 Reorder the terms: 1.330727042 + 2.307142857x + x2 = 928.5714286 + 1.330727042 Combine like terms: 928.5714286 + 1.330727042 = 929.902155642 1.330727042 + 2.307142857x + x2 = 929.902155642 Factor a perfect square on the left side: (x + 1.153571429)(x + 1.153571429) = 929.902155642 Calculate the square root of the right side: 30.4942971 Break this problem into two subproblems by setting (x + 1.153571429) equal to 30.4942971 and -30.4942971.Subproblem 1
x + 1.153571429 = 30.4942971 Simplifying x + 1.153571429 = 30.4942971 Reorder the terms: 1.153571429 + x = 30.4942971 Solving 1.153571429 + x = 30.4942971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.153571429' to each side of the equation. 1.153571429 + -1.153571429 + x = 30.4942971 + -1.153571429 Combine like terms: 1.153571429 + -1.153571429 = 0.000000000 0.000000000 + x = 30.4942971 + -1.153571429 x = 30.4942971 + -1.153571429 Combine like terms: 30.4942971 + -1.153571429 = 29.340725671 x = 29.340725671 Simplifying x = 29.340725671Subproblem 2
x + 1.153571429 = -30.4942971 Simplifying x + 1.153571429 = -30.4942971 Reorder the terms: 1.153571429 + x = -30.4942971 Solving 1.153571429 + x = -30.4942971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.153571429' to each side of the equation. 1.153571429 + -1.153571429 + x = -30.4942971 + -1.153571429 Combine like terms: 1.153571429 + -1.153571429 = 0.000000000 0.000000000 + x = -30.4942971 + -1.153571429 x = -30.4942971 + -1.153571429 Combine like terms: -30.4942971 + -1.153571429 = -31.647868529 x = -31.647868529 Simplifying x = -31.647868529Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.340725671, -31.647868529}
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