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Simplifying x(3 + -8 + 2x) + -4 + -1x = 48 Combine like terms: 3 + -8 = -5 x(-5 + 2x) + -4 + -1x = 48 (-5 * x + 2x * x) + -4 + -1x = 48 (-5x + 2x2) + -4 + -1x = 48 Reorder the terms: -4 + -5x + -1x + 2x2 = 48 Combine like terms: -5x + -1x = -6x -4 + -6x + 2x2 = 48 Solving -4 + -6x + 2x2 = 48 Solving for variable 'x'. Reorder the terms: -4 + -48 + -6x + 2x2 = 48 + -48 Combine like terms: -4 + -48 = -52 -52 + -6x + 2x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -52 + -6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-26 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + -3x + x2)' equal to zero and attempt to solve: Simplifying -26 + -3x + x2 = 0 Solving -26 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -3x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -3x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -3x + x2 = 0 + 26 -3x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -3x + x2 = 26 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 26 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 26 + 2.25 Combine like terms: 26 + 2.25 = 28.25 2.25 + -3x + x2 = 28.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -1.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + -1.5 = 5.315072906 Simplifying x + -1.5 = 5.315072906 Reorder the terms: -1.5 + x = 5.315072906 Solving -1.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.315072906 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.315072906 + 1.5 x = 5.315072906 + 1.5 Combine like terms: 5.315072906 + 1.5 = 6.815072906 x = 6.815072906 Simplifying x = 6.815072906Subproblem 2
x + -1.5 = -5.315072906 Simplifying x + -1.5 = -5.315072906 Reorder the terms: -1.5 + x = -5.315072906 Solving -1.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.315072906 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.315072906 + 1.5 x = -5.315072906 + 1.5 Combine like terms: -5.315072906 + 1.5 = -3.815072906 x = -3.815072906 Simplifying x = -3.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.815072906, -3.815072906}Solution
x = {6.815072906, -3.815072906}
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