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Simplifying x2 + -18x + 5 = 9x + -3 Reorder the terms: 5 + -18x + x2 = 9x + -3 Reorder the terms: 5 + -18x + x2 = -3 + 9x Solving 5 + -18x + x2 = -3 + 9x Solving for variable 'x'. Reorder the terms: 5 + 3 + -18x + -9x + x2 = -3 + 9x + 3 + -9x Combine like terms: 5 + 3 = 8 8 + -18x + -9x + x2 = -3 + 9x + 3 + -9x Combine like terms: -18x + -9x = -27x 8 + -27x + x2 = -3 + 9x + 3 + -9x Reorder the terms: 8 + -27x + x2 = -3 + 3 + 9x + -9x Combine like terms: -3 + 3 = 0 8 + -27x + x2 = 0 + 9x + -9x 8 + -27x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 8 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -27x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -27x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -27x + x2 = 0 + -8 -27x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -27x + x2 = -8 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -8 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -8 + 182.25 Combine like terms: -8 + 182.25 = 174.25 182.25 + -27x + x2 = 174.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + -13.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + -13.5 = 13.200378782 Simplifying x + -13.5 = 13.200378782 Reorder the terms: -13.5 + x = 13.200378782 Solving -13.5 + x = 13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 13.200378782 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 13.200378782 + 13.5 x = 13.200378782 + 13.5 Combine like terms: 13.200378782 + 13.5 = 26.700378782 x = 26.700378782 Simplifying x = 26.700378782Subproblem 2
x + -13.5 = -13.200378782 Simplifying x + -13.5 = -13.200378782 Reorder the terms: -13.5 + x = -13.200378782 Solving -13.5 + x = -13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -13.200378782 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -13.200378782 + 13.5 x = -13.200378782 + 13.5 Combine like terms: -13.200378782 + 13.5 = 0.299621218 x = 0.299621218 Simplifying x = 0.299621218Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.700378782, 0.299621218}
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