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Simplifying 3.14x2 + -1x + -34(3.14) = 0 Multiply -34 * 3.14 3.14x2 + -1x + -106.76 = 0 Reorder the terms: -106.76 + -1x + 3.14x2 = 0 Solving -106.76 + -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'. -34 + -0.3184713376x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + -0.3184713376x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -0.3184713376x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -0.3184713376x + x2 = 0 + 34 -0.3184713376x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -0.3184713376x + x2 = 34 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 = 34 + 0.02535599822 Reorder the terms: 0.02535599822 + -0.3184713376x + x2 = 34 + 0.02535599822 Combine like terms: 34 + 0.02535599822 = 34.02535599822 0.02535599822 + -0.3184713376x + x2 = 34.02535599822 Factor a perfect square on the left side: (x + -0.1592356688)(x + -0.1592356688) = 34.02535599822 Calculate the square root of the right side: 5.833125749 Break this problem into two subproblems by setting (x + -0.1592356688) equal to 5.833125749 and -5.833125749.Subproblem 1
x + -0.1592356688 = 5.833125749 Simplifying x + -0.1592356688 = 5.833125749 Reorder the terms: -0.1592356688 + x = 5.833125749 Solving -0.1592356688 + x = 5.833125749 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 = 5.833125749 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = 5.833125749 + 0.1592356688 x = 5.833125749 + 0.1592356688 Combine like terms: 5.833125749 + 0.1592356688 = 5.9923614178 x = 5.9923614178 Simplifying x = 5.9923614178Subproblem 2
x + -0.1592356688 = -5.833125749 Simplifying x + -0.1592356688 = -5.833125749 Reorder the terms: -0.1592356688 + x = -5.833125749 Solving -0.1592356688 + x = -5.833125749 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 = -5.833125749 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = -5.833125749 + 0.1592356688 x = -5.833125749 + 0.1592356688 Combine like terms: -5.833125749 + 0.1592356688 = -5.6738900802 x = -5.6738900802 Simplifying x = -5.6738900802Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.9923614178, -5.6738900802}
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