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Simplifying x2 + 27x + -210 = 0 Reorder the terms: -210 + 27x + x2 = 0 Solving -210 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + 27x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + 27x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + 27x + x2 = 0 + 210 27x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 27x + x2 = 210 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 = 210 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 210 + 182.25 Combine like terms: 210 + 182.25 = 392.25 182.25 + 27x + x2 = 392.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 392.25 Calculate the square root of the right side: 19.80530232 Break this problem into two subproblems by setting (x + 13.5) equal to 19.80530232 and -19.80530232.Subproblem 1
x + 13.5 = 19.80530232 Simplifying x + 13.5 = 19.80530232 Reorder the terms: 13.5 + x = 19.80530232 Solving 13.5 + x = 19.80530232 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 = 19.80530232 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 19.80530232 + -13.5 x = 19.80530232 + -13.5 Combine like terms: 19.80530232 + -13.5 = 6.30530232 x = 6.30530232 Simplifying x = 6.30530232Subproblem 2
x + 13.5 = -19.80530232 Simplifying x + 13.5 = -19.80530232 Reorder the terms: 13.5 + x = -19.80530232 Solving 13.5 + x = -19.80530232 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 = -19.80530232 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -19.80530232 + -13.5 x = -19.80530232 + -13.5 Combine like terms: -19.80530232 + -13.5 = -33.30530232 x = -33.30530232 Simplifying x = -33.30530232Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.30530232, -33.30530232}
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