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Simplifying x = 6 + -6x(26 + 3x) x = 6 + (26 * -6x + 3x * -6x) x = 6 + (-156x + -18x2) Solving x = 6 + -156x + -18x2 Solving for variable 'x'. Reorder the terms: -6 + x + 156x + 18x2 = 6 + -156x + -18x2 + -6 + 156x + 18x2 Combine like terms: x + 156x = 157x -6 + 157x + 18x2 = 6 + -156x + -18x2 + -6 + 156x + 18x2 Reorder the terms: -6 + 157x + 18x2 = 6 + -6 + -156x + 156x + -18x2 + 18x2 Combine like terms: 6 + -6 = 0 -6 + 157x + 18x2 = 0 + -156x + 156x + -18x2 + 18x2 -6 + 157x + 18x2 = -156x + 156x + -18x2 + 18x2 Combine like terms: -156x + 156x = 0 -6 + 157x + 18x2 = 0 + -18x2 + 18x2 -6 + 157x + 18x2 = -18x2 + 18x2 Combine like terms: -18x2 + 18x2 = 0 -6 + 157x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3333333333 + 8.722222222x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 8.722222222x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 8.722222222x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 8.722222222x + x2 = 0 + 0.3333333333 8.722222222x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 8.722222222x + x2 = 0.3333333333 The x term is 8.722222222x. Take half its coefficient (4.361111111). Square it (19.01929012) and add it to both sides. Add '19.01929012' to each side of the equation. 8.722222222x + 19.01929012 + x2 = 0.3333333333 + 19.01929012 Reorder the terms: 19.01929012 + 8.722222222x + x2 = 0.3333333333 + 19.01929012 Combine like terms: 0.3333333333 + 19.01929012 = 19.3526234533 19.01929012 + 8.722222222x + x2 = 19.3526234533 Factor a perfect square on the left side: (x + 4.361111111)(x + 4.361111111) = 19.3526234533 Calculate the square root of the right side: 4.399161676 Break this problem into two subproblems by setting (x + 4.361111111) equal to 4.399161676 and -4.399161676.Subproblem 1
x + 4.361111111 = 4.399161676 Simplifying x + 4.361111111 = 4.399161676 Reorder the terms: 4.361111111 + x = 4.399161676 Solving 4.361111111 + x = 4.399161676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.361111111' to each side of the equation. 4.361111111 + -4.361111111 + x = 4.399161676 + -4.361111111 Combine like terms: 4.361111111 + -4.361111111 = 0.000000000 0.000000000 + x = 4.399161676 + -4.361111111 x = 4.399161676 + -4.361111111 Combine like terms: 4.399161676 + -4.361111111 = 0.038050565 x = 0.038050565 Simplifying x = 0.038050565Subproblem 2
x + 4.361111111 = -4.399161676 Simplifying x + 4.361111111 = -4.399161676 Reorder the terms: 4.361111111 + x = -4.399161676 Solving 4.361111111 + x = -4.399161676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.361111111' to each side of the equation. 4.361111111 + -4.361111111 + x = -4.399161676 + -4.361111111 Combine like terms: 4.361111111 + -4.361111111 = 0.000000000 0.000000000 + x = -4.399161676 + -4.361111111 x = -4.399161676 + -4.361111111 Combine like terms: -4.399161676 + -4.361111111 = -8.760272787 x = -8.760272787 Simplifying x = -8.760272787Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.038050565, -8.760272787}
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