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Simplifying 2x2 + -6x + -38 = 0 Reorder the terms: -38 + -6x + 2x2 = 0 Solving -38 + -6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + -3x + x2)' equal to zero and attempt to solve: Simplifying -19 + -3x + x2 = 0 Solving -19 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -3x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -3x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -3x + x2 = 0 + 19 -3x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -3x + x2 = 19 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 = 19 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 19 + 2.25 Combine like terms: 19 + 2.25 = 21.25 2.25 + -3x + x2 = 21.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -1.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + -1.5 = 4.609772229 Simplifying x + -1.5 = 4.609772229 Reorder the terms: -1.5 + x = 4.609772229 Solving -1.5 + x = 4.609772229 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 = 4.609772229 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.609772229 + 1.5 x = 4.609772229 + 1.5 Combine like terms: 4.609772229 + 1.5 = 6.109772229 x = 6.109772229 Simplifying x = 6.109772229Subproblem 2
x + -1.5 = -4.609772229 Simplifying x + -1.5 = -4.609772229 Reorder the terms: -1.5 + x = -4.609772229 Solving -1.5 + x = -4.609772229 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 = -4.609772229 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.609772229 + 1.5 x = -4.609772229 + 1.5 Combine like terms: -4.609772229 + 1.5 = -3.109772229 x = -3.109772229 Simplifying x = -3.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.109772229, -3.109772229}Solution
x = {6.109772229, -3.109772229}
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