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Simplifying x2 + 33x + 17 = 0 Reorder the terms: 17 + 33x + x2 = 0 Solving 17 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 33x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 33x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 33x + x2 = 0 + -17 33x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 33x + x2 = -17 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 = -17 + 272.25 Reorder the terms: 272.25 + 33x + x2 = -17 + 272.25 Combine like terms: -17 + 272.25 = 255.25 272.25 + 33x + x2 = 255.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 255.25 Calculate the square root of the right side: 15.976545309 Break this problem into two subproblems by setting (x + 16.5) equal to 15.976545309 and -15.976545309.Subproblem 1
x + 16.5 = 15.976545309 Simplifying x + 16.5 = 15.976545309 Reorder the terms: 16.5 + x = 15.976545309 Solving 16.5 + x = 15.976545309 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 = 15.976545309 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 15.976545309 + -16.5 x = 15.976545309 + -16.5 Combine like terms: 15.976545309 + -16.5 = -0.523454691 x = -0.523454691 Simplifying x = -0.523454691Subproblem 2
x + 16.5 = -15.976545309 Simplifying x + 16.5 = -15.976545309 Reorder the terms: 16.5 + x = -15.976545309 Solving 16.5 + x = -15.976545309 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 = -15.976545309 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -15.976545309 + -16.5 x = -15.976545309 + -16.5 Combine like terms: -15.976545309 + -16.5 = -32.476545309 x = -32.476545309 Simplifying x = -32.476545309Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.523454691, -32.476545309}
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