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Simplifying (18x2) + 26x + 1 = 0 Reorder the terms: 1 + 26x + (18x2) = 0 Solving 1 + 26x + (18x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.05555555556 + 1.444444444x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + 1.444444444x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + 1.444444444x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + 1.444444444x + x2 = 0 + -0.05555555556 1.444444444x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 1.444444444x + x2 = -0.05555555556 The x term is 1.444444444x. Take half its coefficient (0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. 1.444444444x + 0.5216049380 + x2 = -0.05555555556 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444x + x2 = -0.05555555556 + 0.5216049380 Combine like terms: -0.05555555556 + 0.5216049380 = 0.46604938244 0.5216049380 + 1.444444444x + x2 = 0.46604938244 Factor a perfect square on the left side: ((x) + 0.722222222)((x) + 0.722222222) = 0.46604938244 Calculate the square root of the right side: 0.682678096 Break this problem into two subproblems by setting ((x) + 0.722222222) equal to 0.682678096 and -0.682678096.Subproblem 1
(x) + 0.722222222 = 0.682678096 Simplifying (x) + 0.722222222 = 0.682678096 x + 0.722222222 = 0.682678096 Reorder the terms: 0.722222222 + x = 0.682678096 Solving 0.722222222 + x = 0.682678096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = 0.682678096 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 0.682678096 + -0.722222222 x = 0.682678096 + -0.722222222 Combine like terms: 0.682678096 + -0.722222222 = -0.039544126 x = -0.039544126 Simplifying x = -0.039544126Subproblem 2
(x) + 0.722222222 = -0.682678096 Simplifying (x) + 0.722222222 = -0.682678096 x + 0.722222222 = -0.682678096 Reorder the terms: 0.722222222 + x = -0.682678096 Solving 0.722222222 + x = -0.682678096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = -0.682678096 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -0.682678096 + -0.722222222 x = -0.682678096 + -0.722222222 Combine like terms: -0.682678096 + -0.722222222 = -1.404900318 x = -1.404900318 Simplifying x = -1.404900318Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.039544126, -1.404900318}
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