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Simplifying 3.14159265359x2 + -1x + -32(3.14159265359) = 0 Multiply -32 * 3.14159265359 3.14159265359x2 + -1x + -100.5309649 = 0 Reorder the terms: -100.5309649 + -1x + 3.14159265359x2 = 0 Solving -100.5309649 + -1x + 3.14159265359x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.14159265359 the coefficient of the squared term: Divide each side by '3.14159265359'. -32 + -0.3183098862x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -0.3183098862x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -0.3183098862x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -0.3183098862x + x2 = 0 + 32 -0.3183098862x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -0.3183098862x + x2 = 32 The x term is -0.3183098862x. Take half its coefficient (-0.1591549431). Square it (0.02533029591) and add it to both sides. Add '0.02533029591' to each side of the equation. -0.3183098862x + 0.02533029591 + x2 = 32 + 0.02533029591 Reorder the terms: 0.02533029591 + -0.3183098862x + x2 = 32 + 0.02533029591 Combine like terms: 32 + 0.02533029591 = 32.02533029591 0.02533029591 + -0.3183098862x + x2 = 32.02533029591 Factor a perfect square on the left side: (x + -0.1591549431)(x + -0.1591549431) = 32.02533029591 Calculate the square root of the right side: 5.65909271 Break this problem into two subproblems by setting (x + -0.1591549431) equal to 5.65909271 and -5.65909271.Subproblem 1
x + -0.1591549431 = 5.65909271 Simplifying x + -0.1591549431 = 5.65909271 Reorder the terms: -0.1591549431 + x = 5.65909271 Solving -0.1591549431 + x = 5.65909271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1591549431' to each side of the equation. -0.1591549431 + 0.1591549431 + x = 5.65909271 + 0.1591549431 Combine like terms: -0.1591549431 + 0.1591549431 = 0.0000000000 0.0000000000 + x = 5.65909271 + 0.1591549431 x = 5.65909271 + 0.1591549431 Combine like terms: 5.65909271 + 0.1591549431 = 5.8182476531 x = 5.8182476531 Simplifying x = 5.8182476531Subproblem 2
x + -0.1591549431 = -5.65909271 Simplifying x + -0.1591549431 = -5.65909271 Reorder the terms: -0.1591549431 + x = -5.65909271 Solving -0.1591549431 + x = -5.65909271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1591549431' to each side of the equation. -0.1591549431 + 0.1591549431 + x = -5.65909271 + 0.1591549431 Combine like terms: -0.1591549431 + 0.1591549431 = 0.0000000000 0.0000000000 + x = -5.65909271 + 0.1591549431 x = -5.65909271 + 0.1591549431 Combine like terms: -5.65909271 + 0.1591549431 = -5.4999377669 x = -5.4999377669 Simplifying x = -5.4999377669Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.8182476531, -5.4999377669}
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