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Simplifying (2x2 + 3x + -6) + -1(x2 + -18x + 6) = 0 Reorder the terms: (-6 + 3x + 2x2) + -1(x2 + -18x + 6) = 0 Remove parenthesis around (-6 + 3x + 2x2) -6 + 3x + 2x2 + -1(x2 + -18x + 6) = 0 Reorder the terms: -6 + 3x + 2x2 + -1(6 + -18x + x2) = 0 -6 + 3x + 2x2 + (6 * -1 + -18x * -1 + x2 * -1) = 0 -6 + 3x + 2x2 + (-6 + 18x + -1x2) = 0 Reorder the terms: -6 + -6 + 3x + 18x + 2x2 + -1x2 = 0 Combine like terms: -6 + -6 = -12 -12 + 3x + 18x + 2x2 + -1x2 = 0 Combine like terms: 3x + 18x = 21x -12 + 21x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -12 + 21x + 1x2 = 0 Solving -12 + 21x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 21x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 21x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 21x + x2 = 0 + 12 21x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 21x + x2 = 12 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 12 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 12 + 110.25 Combine like terms: 12 + 110.25 = 122.25 110.25 + 21x + x2 = 122.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (x + 10.5) equal to 11.056672194 and -11.056672194.Subproblem 1
x + 10.5 = 11.056672194 Simplifying x + 10.5 = 11.056672194 Reorder the terms: 10.5 + x = 11.056672194 Solving 10.5 + x = 11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 11.056672194 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 11.056672194 + -10.5 x = 11.056672194 + -10.5 Combine like terms: 11.056672194 + -10.5 = 0.556672194 x = 0.556672194 Simplifying x = 0.556672194Subproblem 2
x + 10.5 = -11.056672194 Simplifying x + 10.5 = -11.056672194 Reorder the terms: 10.5 + x = -11.056672194 Solving 10.5 + x = -11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -11.056672194 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -11.056672194 + -10.5 x = -11.056672194 + -10.5 Combine like terms: -11.056672194 + -10.5 = -21.556672194 x = -21.556672194 Simplifying x = -21.556672194Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.556672194, -21.556672194}
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