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Simplifying 18x2 + 36x + -31 = 0 Reorder the terms: -31 + 36x + 18x2 = 0 Solving -31 + 36x + 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'. -1.722222222 + 2x + x2 = 0 Move the constant term to the right: Add '1.722222222' to each side of the equation. -1.722222222 + 2x + 1.722222222 + x2 = 0 + 1.722222222 Reorder the terms: -1.722222222 + 1.722222222 + 2x + x2 = 0 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + 2x + x2 = 0 + 1.722222222 2x + x2 = 0 + 1.722222222 Combine like terms: 0 + 1.722222222 = 1.722222222 2x + x2 = 1.722222222 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.722222222 + 1 Reorder the terms: 1 + 2x + x2 = 1.722222222 + 1 Combine like terms: 1.722222222 + 1 = 2.722222222 1 + 2x + x2 = 2.722222222 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.722222222 Calculate the square root of the right side: 1.649915823 Break this problem into two subproblems by setting (x + 1) equal to 1.649915823 and -1.649915823.Subproblem 1
x + 1 = 1.649915823 Simplifying x + 1 = 1.649915823 Reorder the terms: 1 + x = 1.649915823 Solving 1 + x = 1.649915823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.649915823 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.649915823 + -1 x = 1.649915823 + -1 Combine like terms: 1.649915823 + -1 = 0.649915823 x = 0.649915823 Simplifying x = 0.649915823Subproblem 2
x + 1 = -1.649915823 Simplifying x + 1 = -1.649915823 Reorder the terms: 1 + x = -1.649915823 Solving 1 + x = -1.649915823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.649915823 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.649915823 + -1 x = -1.649915823 + -1 Combine like terms: -1.649915823 + -1 = -2.649915823 x = -2.649915823 Simplifying x = -2.649915823Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.649915823, -2.649915823}
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