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Simplifying x2 + 33x + 31 = 0 Reorder the terms: 31 + 33x + x2 = 0 Solving 31 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 33x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 33x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 33x + x2 = 0 + -31 33x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 33x + x2 = -31 The x term is 33x. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33x + 272.25 + x2 = -31 + 272.25 Reorder the terms: 272.25 + 33x + x2 = -31 + 272.25 Combine like terms: -31 + 272.25 = 241.25 272.25 + 33x + x2 = 241.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 241.25 Calculate the square root of the right side: 15.532224567 Break this problem into two subproblems by setting (x + 16.5) equal to 15.532224567 and -15.532224567.Subproblem 1
x + 16.5 = 15.532224567 Simplifying x + 16.5 = 15.532224567 Reorder the terms: 16.5 + x = 15.532224567 Solving 16.5 + x = 15.532224567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 15.532224567 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 15.532224567 + -16.5 x = 15.532224567 + -16.5 Combine like terms: 15.532224567 + -16.5 = -0.967775433 x = -0.967775433 Simplifying x = -0.967775433Subproblem 2
x + 16.5 = -15.532224567 Simplifying x + 16.5 = -15.532224567 Reorder the terms: 16.5 + x = -15.532224567 Solving 16.5 + x = -15.532224567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -15.532224567 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -15.532224567 + -16.5 x = -15.532224567 + -16.5 Combine like terms: -15.532224567 + -16.5 = -32.032224567 x = -32.032224567 Simplifying x = -32.032224567Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.967775433, -32.032224567}
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