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Simplifying 2x2 + -33x = -5x + -6x + -18 Reorder the terms: -33x + 2x2 = -5x + -6x + -18 Reorder the terms: -33x + 2x2 = -18 + -5x + -6x Combine like terms: -5x + -6x = -11x -33x + 2x2 = -18 + -11x Solving -33x + 2x2 = -18 + -11x Solving for variable 'x'. Reorder the terms: 18 + -33x + 11x + 2x2 = -18 + -11x + 18 + 11x Combine like terms: -33x + 11x = -22x 18 + -22x + 2x2 = -18 + -11x + 18 + 11x Reorder the terms: 18 + -22x + 2x2 = -18 + 18 + -11x + 11x Combine like terms: -18 + 18 = 0 18 + -22x + 2x2 = 0 + -11x + 11x 18 + -22x + 2x2 = -11x + 11x Combine like terms: -11x + 11x = 0 18 + -22x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -11x + x2)' equal to zero and attempt to solve: Simplifying 9 + -11x + x2 = 0 Solving 9 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -11x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -11x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -11x + x2 = 0 + -9 -11x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -11x + x2 = -9 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -9 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -9 + 30.25 Combine like terms: -9 + 30.25 = 21.25 30.25 + -11x + x2 = 21.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -5.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + -5.5 = 4.609772229 Simplifying x + -5.5 = 4.609772229 Reorder the terms: -5.5 + x = 4.609772229 Solving -5.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 4.609772229 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.609772229 + 5.5 x = 4.609772229 + 5.5 Combine like terms: 4.609772229 + 5.5 = 10.109772229 x = 10.109772229 Simplifying x = 10.109772229Subproblem 2
x + -5.5 = -4.609772229 Simplifying x + -5.5 = -4.609772229 Reorder the terms: -5.5 + x = -4.609772229 Solving -5.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -4.609772229 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.609772229 + 5.5 x = -4.609772229 + 5.5 Combine like terms: -4.609772229 + 5.5 = 0.890227771 x = 0.890227771 Simplifying x = 0.890227771Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.109772229, 0.890227771}Solution
x = {10.109772229, 0.890227771}
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