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Simplifying 54x2 + -11x + -7 = 0 Reorder the terms: -7 + -11x + 54x2 = 0 Solving -7 + -11x + 54x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.1296296296 + -0.2037037037x + x2 = 0 Move the constant term to the right: Add '0.1296296296' to each side of the equation. -0.1296296296 + -0.2037037037x + 0.1296296296 + x2 = 0 + 0.1296296296 Reorder the terms: -0.1296296296 + 0.1296296296 + -0.2037037037x + x2 = 0 + 0.1296296296 Combine like terms: -0.1296296296 + 0.1296296296 = 0.0000000000 0.0000000000 + -0.2037037037x + x2 = 0 + 0.1296296296 -0.2037037037x + x2 = 0 + 0.1296296296 Combine like terms: 0 + 0.1296296296 = 0.1296296296 -0.2037037037x + x2 = 0.1296296296 The x term is -0.2037037037x. Take half its coefficient (-0.1018518519). Square it (0.01037379974) and add it to both sides. Add '0.01037379974' to each side of the equation. -0.2037037037x + 0.01037379974 + x2 = 0.1296296296 + 0.01037379974 Reorder the terms: 0.01037379974 + -0.2037037037x + x2 = 0.1296296296 + 0.01037379974 Combine like terms: 0.1296296296 + 0.01037379974 = 0.14000342934 0.01037379974 + -0.2037037037x + x2 = 0.14000342934 Factor a perfect square on the left side: (x + -0.1018518519)(x + -0.1018518519) = 0.14000342934 Calculate the square root of the right side: 0.374170321 Break this problem into two subproblems by setting (x + -0.1018518519) equal to 0.374170321 and -0.374170321.Subproblem 1
x + -0.1018518519 = 0.374170321 Simplifying x + -0.1018518519 = 0.374170321 Reorder the terms: -0.1018518519 + x = 0.374170321 Solving -0.1018518519 + x = 0.374170321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1018518519' to each side of the equation. -0.1018518519 + 0.1018518519 + x = 0.374170321 + 0.1018518519 Combine like terms: -0.1018518519 + 0.1018518519 = 0.0000000000 0.0000000000 + x = 0.374170321 + 0.1018518519 x = 0.374170321 + 0.1018518519 Combine like terms: 0.374170321 + 0.1018518519 = 0.4760221729 x = 0.4760221729 Simplifying x = 0.4760221729Subproblem 2
x + -0.1018518519 = -0.374170321 Simplifying x + -0.1018518519 = -0.374170321 Reorder the terms: -0.1018518519 + x = -0.374170321 Solving -0.1018518519 + x = -0.374170321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1018518519' to each side of the equation. -0.1018518519 + 0.1018518519 + x = -0.374170321 + 0.1018518519 Combine like terms: -0.1018518519 + 0.1018518519 = 0.0000000000 0.0000000000 + x = -0.374170321 + 0.1018518519 x = -0.374170321 + 0.1018518519 Combine like terms: -0.374170321 + 0.1018518519 = -0.2723184691 x = -0.2723184691 Simplifying x = -0.2723184691Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4760221729, -0.2723184691}
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