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Simplifying (3.14159) * x2 + 18(3.14159) * x + -108 = 0 Multiply 18 * 3.14159 3.14159x2 + 56.54862x + -108 = 0 Reorder the terms: -108 + 56.54862x + 3.14159x2 = 0 Solving -108 + 56.54862x + 3.14159x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.14159 the coefficient of the squared term: Divide each side by '3.14159'. -34.37749675 + 18x + x2 = 0 Move the constant term to the right: Add '34.37749675' to each side of the equation. -34.37749675 + 18x + 34.37749675 + x2 = 0 + 34.37749675 Reorder the terms: -34.37749675 + 34.37749675 + 18x + x2 = 0 + 34.37749675 Combine like terms: -34.37749675 + 34.37749675 = 0.00000000 0.00000000 + 18x + x2 = 0 + 34.37749675 18x + x2 = 0 + 34.37749675 Combine like terms: 0 + 34.37749675 = 34.37749675 18x + x2 = 34.37749675 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 34.37749675 + 81 Reorder the terms: 81 + 18x + x2 = 34.37749675 + 81 Combine like terms: 34.37749675 + 81 = 115.37749675 81 + 18x + x2 = 115.37749675 Factor a perfect square on the left side: (x + 9)(x + 9) = 115.37749675 Calculate the square root of the right side: 10.741391751 Break this problem into two subproblems by setting (x + 9) equal to 10.741391751 and -10.741391751.Subproblem 1
x + 9 = 10.741391751 Simplifying x + 9 = 10.741391751 Reorder the terms: 9 + x = 10.741391751 Solving 9 + x = 10.741391751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 10.741391751 + -9 Combine like terms: 9 + -9 = 0 0 + x = 10.741391751 + -9 x = 10.741391751 + -9 Combine like terms: 10.741391751 + -9 = 1.741391751 x = 1.741391751 Simplifying x = 1.741391751Subproblem 2
x + 9 = -10.741391751 Simplifying x + 9 = -10.741391751 Reorder the terms: 9 + x = -10.741391751 Solving 9 + x = -10.741391751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -10.741391751 + -9 Combine like terms: 9 + -9 = 0 0 + x = -10.741391751 + -9 x = -10.741391751 + -9 Combine like terms: -10.741391751 + -9 = -19.741391751 x = -19.741391751 Simplifying x = -19.741391751Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.741391751, -19.741391751}
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