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Simplifying x2 + -33x + -270 = 0 Reorder the terms: -270 + -33x + x2 = 0 Solving -270 + -33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + -33x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + -33x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + -33x + x2 = 0 + 270 -33x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 -33x + x2 = 270 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 = 270 + 272.25 Reorder the terms: 272.25 + -33x + x2 = 270 + 272.25 Combine like terms: 270 + 272.25 = 542.25 272.25 + -33x + x2 = 542.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 542.25 Calculate the square root of the right side: 23.286262044 Break this problem into two subproblems by setting (x + -16.5) equal to 23.286262044 and -23.286262044.Subproblem 1
x + -16.5 = 23.286262044 Simplifying x + -16.5 = 23.286262044 Reorder the terms: -16.5 + x = 23.286262044 Solving -16.5 + x = 23.286262044 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 = 23.286262044 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 23.286262044 + 16.5 x = 23.286262044 + 16.5 Combine like terms: 23.286262044 + 16.5 = 39.786262044 x = 39.786262044 Simplifying x = 39.786262044Subproblem 2
x + -16.5 = -23.286262044 Simplifying x + -16.5 = -23.286262044 Reorder the terms: -16.5 + x = -23.286262044 Solving -16.5 + x = -23.286262044 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 = -23.286262044 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -23.286262044 + 16.5 x = -23.286262044 + 16.5 Combine like terms: -23.286262044 + 16.5 = -6.786262044 x = -6.786262044 Simplifying x = -6.786262044Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.786262044, -6.786262044}
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