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Simplifying 18x2 + 17 = 40x Reorder the terms: 17 + 18x2 = 40x Solving 17 + 18x2 = 40x Solving for variable 'x'. Reorder the terms: 17 + -40x + 18x2 = 40x + -40x Combine like terms: 40x + -40x = 0 17 + -40x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.9444444444 + -2.222222222x + x2 = 0 Move the constant term to the right: Add '-0.9444444444' to each side of the equation. 0.9444444444 + -2.222222222x + -0.9444444444 + x2 = 0 + -0.9444444444 Reorder the terms: 0.9444444444 + -0.9444444444 + -2.222222222x + x2 = 0 + -0.9444444444 Combine like terms: 0.9444444444 + -0.9444444444 = 0.0000000000 0.0000000000 + -2.222222222x + x2 = 0 + -0.9444444444 -2.222222222x + x2 = 0 + -0.9444444444 Combine like terms: 0 + -0.9444444444 = -0.9444444444 -2.222222222x + x2 = -0.9444444444 The x term is -2.222222222x. Take half its coefficient (-1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. -2.222222222x + 1.234567901 + x2 = -0.9444444444 + 1.234567901 Reorder the terms: 1.234567901 + -2.222222222x + x2 = -0.9444444444 + 1.234567901 Combine like terms: -0.9444444444 + 1.234567901 = 0.2901234566 1.234567901 + -2.222222222x + x2 = 0.2901234566 Factor a perfect square on the left side: (x + -1.111111111)(x + -1.111111111) = 0.2901234566 Calculate the square root of the right side: 0.538631095 Break this problem into two subproblems by setting (x + -1.111111111) equal to 0.538631095 and -0.538631095.Subproblem 1
x + -1.111111111 = 0.538631095 Simplifying x + -1.111111111 = 0.538631095 Reorder the terms: -1.111111111 + x = 0.538631095 Solving -1.111111111 + x = 0.538631095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = 0.538631095 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = 0.538631095 + 1.111111111 x = 0.538631095 + 1.111111111 Combine like terms: 0.538631095 + 1.111111111 = 1.649742206 x = 1.649742206 Simplifying x = 1.649742206Subproblem 2
x + -1.111111111 = -0.538631095 Simplifying x + -1.111111111 = -0.538631095 Reorder the terms: -1.111111111 + x = -0.538631095 Solving -1.111111111 + x = -0.538631095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = -0.538631095 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = -0.538631095 + 1.111111111 x = -0.538631095 + 1.111111111 Combine like terms: -0.538631095 + 1.111111111 = 0.572480016 x = 0.572480016 Simplifying x = 0.572480016Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.649742206, 0.572480016}
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