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Simplifying x2 + 33x + -260 = 0 Reorder the terms: -260 + 33x + x2 = 0 Solving -260 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '260' to each side of the equation. -260 + 33x + 260 + x2 = 0 + 260 Reorder the terms: -260 + 260 + 33x + x2 = 0 + 260 Combine like terms: -260 + 260 = 0 0 + 33x + x2 = 0 + 260 33x + x2 = 0 + 260 Combine like terms: 0 + 260 = 260 33x + x2 = 260 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 = 260 + 272.25 Reorder the terms: 272.25 + 33x + x2 = 260 + 272.25 Combine like terms: 260 + 272.25 = 532.25 272.25 + 33x + x2 = 532.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 532.25 Calculate the square root of the right side: 23.07054399 Break this problem into two subproblems by setting (x + 16.5) equal to 23.07054399 and -23.07054399.Subproblem 1
x + 16.5 = 23.07054399 Simplifying x + 16.5 = 23.07054399 Reorder the terms: 16.5 + x = 23.07054399 Solving 16.5 + x = 23.07054399 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 = 23.07054399 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 23.07054399 + -16.5 x = 23.07054399 + -16.5 Combine like terms: 23.07054399 + -16.5 = 6.57054399 x = 6.57054399 Simplifying x = 6.57054399Subproblem 2
x + 16.5 = -23.07054399 Simplifying x + 16.5 = -23.07054399 Reorder the terms: 16.5 + x = -23.07054399 Solving 16.5 + x = -23.07054399 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 = -23.07054399 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -23.07054399 + -16.5 x = -23.07054399 + -16.5 Combine like terms: -23.07054399 + -16.5 = -39.57054399 x = -39.57054399 Simplifying x = -39.57054399Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.57054399, -39.57054399}
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