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Simplifying 3.14159265359x2 + 18(3.14159265359) * x + -108 = 0 Multiply 18 * 3.14159265359 3.14159265359x2 + 56.54866776x + -108 = 0 Reorder the terms: -108 + 56.54866776x + 3.14159265359x2 = 0 Solving -108 + 56.54866776x + 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'. -34.37746771 + 18x + x2 = 0 Move the constant term to the right: Add '34.37746771' to each side of the equation. -34.37746771 + 18x + 34.37746771 + x2 = 0 + 34.37746771 Reorder the terms: -34.37746771 + 34.37746771 + 18x + x2 = 0 + 34.37746771 Combine like terms: -34.37746771 + 34.37746771 = 0.00000000 0.00000000 + 18x + x2 = 0 + 34.37746771 18x + x2 = 0 + 34.37746771 Combine like terms: 0 + 34.37746771 = 34.37746771 18x + x2 = 34.37746771 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 = 34.37746771 + 81 Reorder the terms: 81 + 18x + x2 = 34.37746771 + 81 Combine like terms: 34.37746771 + 81 = 115.37746771 81 + 18x + x2 = 115.37746771 Factor a perfect square on the left side: (x + 9)(x + 9) = 115.37746771 Calculate the square root of the right side: 10.741390399 Break this problem into two subproblems by setting (x + 9) equal to 10.741390399 and -10.741390399.Subproblem 1
x + 9 = 10.741390399 Simplifying x + 9 = 10.741390399 Reorder the terms: 9 + x = 10.741390399 Solving 9 + x = 10.741390399 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 = 10.741390399 + -9 Combine like terms: 9 + -9 = 0 0 + x = 10.741390399 + -9 x = 10.741390399 + -9 Combine like terms: 10.741390399 + -9 = 1.741390399 x = 1.741390399 Simplifying x = 1.741390399Subproblem 2
x + 9 = -10.741390399 Simplifying x + 9 = -10.741390399 Reorder the terms: 9 + x = -10.741390399 Solving 9 + x = -10.741390399 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 = -10.741390399 + -9 Combine like terms: 9 + -9 = 0 0 + x = -10.741390399 + -9 x = -10.741390399 + -9 Combine like terms: -10.741390399 + -9 = -19.741390399 x = -19.741390399 Simplifying x = -19.741390399Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.741390399, -19.741390399}
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