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Simplifying 3.14159265359x2 + -1x + -38(3.14159265359) = 0 Multiply -38 * 3.14159265359 3.14159265359x2 + -1x + -119.3805208 = 0 Reorder the terms: -119.3805208 + -1x + 3.14159265359x2 = 0 Solving -119.3805208 + -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'. -37.99999999 + -0.3183098862x + x2 = 0 Move the constant term to the right: Add '37.99999999' to each side of the equation. -37.99999999 + -0.3183098862x + 37.99999999 + x2 = 0 + 37.99999999 Reorder the terms: -37.99999999 + 37.99999999 + -0.3183098862x + x2 = 0 + 37.99999999 Combine like terms: -37.99999999 + 37.99999999 = 0.00000000 0.00000000 + -0.3183098862x + x2 = 0 + 37.99999999 -0.3183098862x + x2 = 0 + 37.99999999 Combine like terms: 0 + 37.99999999 = 37.99999999 -0.3183098862x + x2 = 37.99999999 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 = 37.99999999 + 0.02533029591 Reorder the terms: 0.02533029591 + -0.3183098862x + x2 = 37.99999999 + 0.02533029591 Combine like terms: 37.99999999 + 0.02533029591 = 38.02533028591 0.02533029591 + -0.3183098862x + x2 = 38.02533028591 Factor a perfect square on the left side: (x + -0.1591549431)(x + -0.1591549431) = 38.02533028591 Calculate the square root of the right side: 6.166468218 Break this problem into two subproblems by setting (x + -0.1591549431) equal to 6.166468218 and -6.166468218.Subproblem 1
x + -0.1591549431 = 6.166468218 Simplifying x + -0.1591549431 = 6.166468218 Reorder the terms: -0.1591549431 + x = 6.166468218 Solving -0.1591549431 + x = 6.166468218 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 = 6.166468218 + 0.1591549431 Combine like terms: -0.1591549431 + 0.1591549431 = 0.0000000000 0.0000000000 + x = 6.166468218 + 0.1591549431 x = 6.166468218 + 0.1591549431 Combine like terms: 6.166468218 + 0.1591549431 = 6.3256231611 x = 6.3256231611 Simplifying x = 6.3256231611Subproblem 2
x + -0.1591549431 = -6.166468218 Simplifying x + -0.1591549431 = -6.166468218 Reorder the terms: -0.1591549431 + x = -6.166468218 Solving -0.1591549431 + x = -6.166468218 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 = -6.166468218 + 0.1591549431 Combine like terms: -0.1591549431 + 0.1591549431 = 0.0000000000 0.0000000000 + x = -6.166468218 + 0.1591549431 x = -6.166468218 + 0.1591549431 Combine like terms: -6.166468218 + 0.1591549431 = -6.0073132749 x = -6.0073132749 Simplifying x = -6.0073132749Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.3256231611, -6.0073132749}
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