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Simplifying x2 + 33x + -13 = 0 Reorder the terms: -13 + 33x + x2 = 0 Solving -13 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 33x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 33x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 33x + x2 = 0 + 13 33x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 33x + x2 = 13 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 = 13 + 272.25 Reorder the terms: 272.25 + 33x + x2 = 13 + 272.25 Combine like terms: 13 + 272.25 = 285.25 272.25 + 33x + x2 = 285.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 285.25 Calculate the square root of the right side: 16.889345754 Break this problem into two subproblems by setting (x + 16.5) equal to 16.889345754 and -16.889345754.Subproblem 1
x + 16.5 = 16.889345754 Simplifying x + 16.5 = 16.889345754 Reorder the terms: 16.5 + x = 16.889345754 Solving 16.5 + x = 16.889345754 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 = 16.889345754 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 16.889345754 + -16.5 x = 16.889345754 + -16.5 Combine like terms: 16.889345754 + -16.5 = 0.389345754 x = 0.389345754 Simplifying x = 0.389345754Subproblem 2
x + 16.5 = -16.889345754 Simplifying x + 16.5 = -16.889345754 Reorder the terms: 16.5 + x = -16.889345754 Solving 16.5 + x = -16.889345754 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 = -16.889345754 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -16.889345754 + -16.5 x = -16.889345754 + -16.5 Combine like terms: -16.889345754 + -16.5 = -33.389345754 x = -33.389345754 Simplifying x = -33.389345754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.389345754, -33.389345754}
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