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Simplifying x2 + 9x + -255 = 0 Reorder the terms: -255 + 9x + x2 = 0 Solving -255 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '255' to each side of the equation. -255 + 9x + 255 + x2 = 0 + 255 Reorder the terms: -255 + 255 + 9x + x2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + 9x + x2 = 0 + 255 9x + x2 = 0 + 255 Combine like terms: 0 + 255 = 255 9x + x2 = 255 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 255 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 255 + 20.25 Combine like terms: 255 + 20.25 = 275.25 20.25 + 9x + x2 = 275.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 275.25 Calculate the square root of the right side: 16.590660023 Break this problem into two subproblems by setting (x + 4.5) equal to 16.590660023 and -16.590660023.Subproblem 1
x + 4.5 = 16.590660023 Simplifying x + 4.5 = 16.590660023 Reorder the terms: 4.5 + x = 16.590660023 Solving 4.5 + x = 16.590660023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 16.590660023 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 16.590660023 + -4.5 x = 16.590660023 + -4.5 Combine like terms: 16.590660023 + -4.5 = 12.090660023 x = 12.090660023 Simplifying x = 12.090660023Subproblem 2
x + 4.5 = -16.590660023 Simplifying x + 4.5 = -16.590660023 Reorder the terms: 4.5 + x = -16.590660023 Solving 4.5 + x = -16.590660023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -16.590660023 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -16.590660023 + -4.5 x = -16.590660023 + -4.5 Combine like terms: -16.590660023 + -4.5 = -21.090660023 x = -21.090660023 Simplifying x = -21.090660023Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.090660023, -21.090660023}
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