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Simplifying 3.14x2 + -1x + -1(32 * 3.14) = 0 Multiply 32 * 3.14 3.14x2 + -1x + -1(100.48) = 0 Multiply -1 * 100.48 3.14x2 + -1x + -100.48 = 0 Reorder the terms: -100.48 + -1x + 3.14x2 = 0 Solving -100.48 + -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'. -32 + -0.3184713376x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -0.3184713376x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -0.3184713376x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -0.3184713376x + x2 = 0 + 32 -0.3184713376x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -0.3184713376x + x2 = 32 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 = 32 + 0.02535599822 Reorder the terms: 0.02535599822 + -0.3184713376x + x2 = 32 + 0.02535599822 Combine like terms: 32 + 0.02535599822 = 32.02535599822 0.02535599822 + -0.3184713376x + x2 = 32.02535599822 Factor a perfect square on the left side: (x + -0.1592356688)(x + -0.1592356688) = 32.02535599822 Calculate the square root of the right side: 5.65909498 Break this problem into two subproblems by setting (x + -0.1592356688) equal to 5.65909498 and -5.65909498.Subproblem 1
x + -0.1592356688 = 5.65909498 Simplifying x + -0.1592356688 = 5.65909498 Reorder the terms: -0.1592356688 + x = 5.65909498 Solving -0.1592356688 + x = 5.65909498 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 = 5.65909498 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = 5.65909498 + 0.1592356688 x = 5.65909498 + 0.1592356688 Combine like terms: 5.65909498 + 0.1592356688 = 5.8183306488 x = 5.8183306488 Simplifying x = 5.8183306488Subproblem 2
x + -0.1592356688 = -5.65909498 Simplifying x + -0.1592356688 = -5.65909498 Reorder the terms: -0.1592356688 + x = -5.65909498 Solving -0.1592356688 + x = -5.65909498 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 = -5.65909498 + 0.1592356688 Combine like terms: -0.1592356688 + 0.1592356688 = 0.0000000000 0.0000000000 + x = -5.65909498 + 0.1592356688 x = -5.65909498 + 0.1592356688 Combine like terms: -5.65909498 + 0.1592356688 = -5.4998593112 x = -5.4998593112 Simplifying x = -5.4998593112Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.8183306488, -5.4998593112}
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