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Simplifying 18x2 + 31x + -40 = 0 Reorder the terms: -40 + 31x + 18x2 = 0 Solving -40 + 31x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -2.222222222 + 1.722222222x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 1.722222222x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 1.722222222x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 1.722222222x + x2 = 0 + 2.222222222 1.722222222x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 1.722222222x + x2 = 2.222222222 The x term is 1.722222222x. Take half its coefficient (0.861111111). Square it (0.7415123455) and add it to both sides. Add '0.7415123455' to each side of the equation. 1.722222222x + 0.7415123455 + x2 = 2.222222222 + 0.7415123455 Reorder the terms: 0.7415123455 + 1.722222222x + x2 = 2.222222222 + 0.7415123455 Combine like terms: 2.222222222 + 0.7415123455 = 2.9637345675 0.7415123455 + 1.722222222x + x2 = 2.9637345675 Factor a perfect square on the left side: (x + 0.861111111)(x + 0.861111111) = 2.9637345675 Calculate the square root of the right side: 1.721550048 Break this problem into two subproblems by setting (x + 0.861111111) equal to 1.721550048 and -1.721550048.Subproblem 1
x + 0.861111111 = 1.721550048 Simplifying x + 0.861111111 = 1.721550048 Reorder the terms: 0.861111111 + x = 1.721550048 Solving 0.861111111 + x = 1.721550048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.861111111' to each side of the equation. 0.861111111 + -0.861111111 + x = 1.721550048 + -0.861111111 Combine like terms: 0.861111111 + -0.861111111 = 0.000000000 0.000000000 + x = 1.721550048 + -0.861111111 x = 1.721550048 + -0.861111111 Combine like terms: 1.721550048 + -0.861111111 = 0.860438937 x = 0.860438937 Simplifying x = 0.860438937Subproblem 2
x + 0.861111111 = -1.721550048 Simplifying x + 0.861111111 = -1.721550048 Reorder the terms: 0.861111111 + x = -1.721550048 Solving 0.861111111 + x = -1.721550048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.861111111' to each side of the equation. 0.861111111 + -0.861111111 + x = -1.721550048 + -0.861111111 Combine like terms: 0.861111111 + -0.861111111 = 0.000000000 0.000000000 + x = -1.721550048 + -0.861111111 x = -1.721550048 + -0.861111111 Combine like terms: -1.721550048 + -0.861111111 = -2.582661159 x = -2.582661159 Simplifying x = -2.582661159Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.860438937, -2.582661159}
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