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Simplifying (9x2) + x + -55 = 0 Reorder the terms: -55 + x + (9x2) = 0 Solving -55 + x + (9x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.111111111 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '6.111111111' to each side of the equation. -6.111111111 + 0.1111111111x + 6.111111111 + x2 = 0 + 6.111111111 Reorder the terms: -6.111111111 + 6.111111111 + 0.1111111111x + x2 = 0 + 6.111111111 Combine like terms: -6.111111111 + 6.111111111 = 0.000000000 0.000000000 + 0.1111111111x + x2 = 0 + 6.111111111 0.1111111111x + x2 = 0 + 6.111111111 Combine like terms: 0 + 6.111111111 = 6.111111111 0.1111111111x + x2 = 6.111111111 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x + 0.25 + x2 = 6.111111111 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = 6.111111111 + 0.25 Combine like terms: 6.111111111 + 0.25 = 6.361111111 0.25 + 0.1111111111x + x2 = 6.361111111 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 6.361111111 Calculate the square root of the right side: 2.522124325 Break this problem into two subproblems by setting ((x) + 0.5) equal to 2.522124325 and -2.522124325.Subproblem 1
(x) + 0.5 = 2.522124325 Simplifying (x) + 0.5 = 2.522124325 x + 0.5 = 2.522124325 Reorder the terms: 0.5 + x = 2.522124325 Solving 0.5 + x = 2.522124325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.522124325 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.522124325 + -0.5 x = 2.522124325 + -0.5 Combine like terms: 2.522124325 + -0.5 = 2.022124325 x = 2.022124325 Simplifying x = 2.022124325Subproblem 2
(x) + 0.5 = -2.522124325 Simplifying (x) + 0.5 = -2.522124325 x + 0.5 = -2.522124325 Reorder the terms: 0.5 + x = -2.522124325 Solving 0.5 + x = -2.522124325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.522124325 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.522124325 + -0.5 x = -2.522124325 + -0.5 Combine like terms: -2.522124325 + -0.5 = -3.022124325 x = -3.022124325 Simplifying x = -3.022124325Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.022124325, -3.022124325}
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