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Simplifying 2x2 + -54x + -38 = 0 Reorder the terms: -38 + -54x + 2x2 = 0 Solving -38 + -54x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + -27x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + -27x + x2)' equal to zero and attempt to solve: Simplifying -19 + -27x + x2 = 0 Solving -19 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -27x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -27x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -27x + x2 = 0 + 19 -27x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -27x + x2 = 19 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = 19 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 19 + 182.25 Combine like terms: 19 + 182.25 = 201.25 182.25 + -27x + x2 = 201.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 201.25 Calculate the square root of the right side: 14.186260959 Break this problem into two subproblems by setting (x + -13.5) equal to 14.186260959 and -14.186260959.Subproblem 1
x + -13.5 = 14.186260959 Simplifying x + -13.5 = 14.186260959 Reorder the terms: -13.5 + x = 14.186260959 Solving -13.5 + x = 14.186260959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 14.186260959 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 14.186260959 + 13.5 x = 14.186260959 + 13.5 Combine like terms: 14.186260959 + 13.5 = 27.686260959 x = 27.686260959 Simplifying x = 27.686260959Subproblem 2
x + -13.5 = -14.186260959 Simplifying x + -13.5 = -14.186260959 Reorder the terms: -13.5 + x = -14.186260959 Solving -13.5 + x = -14.186260959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -14.186260959 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -14.186260959 + 13.5 x = -14.186260959 + 13.5 Combine like terms: -14.186260959 + 13.5 = -0.686260959 x = -0.686260959 Simplifying x = -0.686260959Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.686260959, -0.686260959}Solution
x = {27.686260959, -0.686260959}
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