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Simplifying x2 + 33x + 37 = 0 Reorder the terms: 37 + 33x + x2 = 0 Solving 37 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 33x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 33x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 33x + x2 = 0 + -37 33x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 33x + x2 = -37 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 = -37 + 272.25 Reorder the terms: 272.25 + 33x + x2 = -37 + 272.25 Combine like terms: -37 + 272.25 = 235.25 272.25 + 33x + x2 = 235.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 235.25 Calculate the square root of the right side: 15.33786165 Break this problem into two subproblems by setting (x + 16.5) equal to 15.33786165 and -15.33786165.Subproblem 1
x + 16.5 = 15.33786165 Simplifying x + 16.5 = 15.33786165 Reorder the terms: 16.5 + x = 15.33786165 Solving 16.5 + x = 15.33786165 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 = 15.33786165 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 15.33786165 + -16.5 x = 15.33786165 + -16.5 Combine like terms: 15.33786165 + -16.5 = -1.16213835 x = -1.16213835 Simplifying x = -1.16213835Subproblem 2
x + 16.5 = -15.33786165 Simplifying x + 16.5 = -15.33786165 Reorder the terms: 16.5 + x = -15.33786165 Solving 16.5 + x = -15.33786165 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 = -15.33786165 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -15.33786165 + -16.5 x = -15.33786165 + -16.5 Combine like terms: -15.33786165 + -16.5 = -31.83786165 x = -31.83786165 Simplifying x = -31.83786165Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.16213835, -31.83786165}
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