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Simplifying 3.14x2 + -1x + -96(3.14) = 0 Multiply -96 * 3.14 3.14x2 + -1x + -301.44 = 0 Reorder the terms: -301.44 + -1x + 3.14x2 = 0 Solving -301.44 + -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'. -96 + -0.3184713376x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + -0.3184713376x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -0.3184713376x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -0.3184713376x + x2 = 0 + 96 -0.3184713376x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -0.3184713376x + x2 = 96 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 = 96 + 0.02535599822 Reorder the terms: 0.02535599822 + -0.3184713376x + x2 = 96 + 0.02535599822 Combine like terms: 96 + 0.02535599822 = 96.02535599822 0.02535599822 + -0.3184713376x + x2 = 96.02535599822 Factor a perfect square on the left side: (x + -0.1592356688)(x + -0.1592356688) = 96.02535599822 Calculate the square root of the right side: 9.799252829 Break this problem into two subproblems by setting (x + -0.1592356688) equal to 9.799252829 and -9.799252829.Subproblem 1
x + -0.1592356688 = 9.799252829 Simplifying x + -0.1592356688 = 9.799252829 Reorder the terms: -0.1592356688 + x = 9.799252829 Solving -0.1592356688 + x = 9.799252829 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 = 9.799252829 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = 9.799252829 + 0.1592356688 x = 9.799252829 + 0.1592356688 Combine like terms: 9.799252829 + 0.1592356688 = 9.9584884978 x = 9.9584884978 Simplifying x = 9.9584884978Subproblem 2
x + -0.1592356688 = -9.799252829 Simplifying x + -0.1592356688 = -9.799252829 Reorder the terms: -0.1592356688 + x = -9.799252829 Solving -0.1592356688 + x = -9.799252829 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 = -9.799252829 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = -9.799252829 + 0.1592356688 x = -9.799252829 + 0.1592356688 Combine like terms: -9.799252829 + 0.1592356688 = -9.6400171602 x = -9.6400171602 Simplifying x = -9.6400171602Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.9584884978, -9.6400171602}
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