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Simplifying 3.14x2 + -1x + -1(14 * 3.14) = 0 Multiply 14 * 3.14 3.14x2 + -1x + -1(43.96) = 0 Multiply -1 * 43.96 3.14x2 + -1x + -43.96 = 0 Reorder the terms: -43.96 + -1x + 3.14x2 = 0 Solving -43.96 + -1x + 3.14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.14 the coefficient of the squared term: Divide each side by '3.14'. -14 + -0.3184713376x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -0.3184713376x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -0.3184713376x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -0.3184713376x + x2 = 0 + 14 -0.3184713376x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -0.3184713376x + x2 = 14 The x term is -0.3184713376x. Take half its coefficient (-0.1592356688). Square it (0.02535599822) and add it to both sides. Add '0.02535599822' to each side of the equation. -0.3184713376x + 0.02535599822 + x2 = 14 + 0.02535599822 Reorder the terms: 0.02535599822 + -0.3184713376x + x2 = 14 + 0.02535599822 Combine like terms: 14 + 0.02535599822 = 14.02535599822 0.02535599822 + -0.3184713376x + x2 = 14.02535599822 Factor a perfect square on the left side: (x + -0.1592356688)(x + -0.1592356688) = 14.02535599822 Calculate the square root of the right side: 3.745044192 Break this problem into two subproblems by setting (x + -0.1592356688) equal to 3.745044192 and -3.745044192.Subproblem 1
x + -0.1592356688 = 3.745044192 Simplifying x + -0.1592356688 = 3.745044192 Reorder the terms: -0.1592356688 + x = 3.745044192 Solving -0.1592356688 + x = 3.745044192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1592356688' to each side of the equation. -0.1592356688 + 0.1592356688 + x = 3.745044192 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = 3.745044192 + 0.1592356688 x = 3.745044192 + 0.1592356688 Combine like terms: 3.745044192 + 0.1592356688 = 3.9042798608 x = 3.9042798608 Simplifying x = 3.9042798608Subproblem 2
x + -0.1592356688 = -3.745044192 Simplifying x + -0.1592356688 = -3.745044192 Reorder the terms: -0.1592356688 + x = -3.745044192 Solving -0.1592356688 + x = -3.745044192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1592356688' to each side of the equation. -0.1592356688 + 0.1592356688 + x = -3.745044192 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = -3.745044192 + 0.1592356688 x = -3.745044192 + 0.1592356688 Combine like terms: -3.745044192 + 0.1592356688 = -3.5858085232 x = -3.5858085232 Simplifying x = -3.5858085232Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9042798608, -3.5858085232}
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