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Simplifying 2x2 + -110x + 204 = 0 Reorder the terms: 204 + -110x + 2x2 = 0 Solving 204 + -110x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(102 + -55x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(102 + -55x + x2)' equal to zero and attempt to solve: Simplifying 102 + -55x + x2 = 0 Solving 102 + -55x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-102' to each side of the equation. 102 + -55x + -102 + x2 = 0 + -102 Reorder the terms: 102 + -102 + -55x + x2 = 0 + -102 Combine like terms: 102 + -102 = 0 0 + -55x + x2 = 0 + -102 -55x + x2 = 0 + -102 Combine like terms: 0 + -102 = -102 -55x + x2 = -102 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = -102 + 756.25 Reorder the terms: 756.25 + -55x + x2 = -102 + 756.25 Combine like terms: -102 + 756.25 = 654.25 756.25 + -55x + x2 = 654.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 654.25 Calculate the square root of the right side: 25.578311125 Break this problem into two subproblems by setting (x + -27.5) equal to 25.578311125 and -25.578311125.Subproblem 1
x + -27.5 = 25.578311125 Simplifying x + -27.5 = 25.578311125 Reorder the terms: -27.5 + x = 25.578311125 Solving -27.5 + x = 25.578311125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 25.578311125 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 25.578311125 + 27.5 x = 25.578311125 + 27.5 Combine like terms: 25.578311125 + 27.5 = 53.078311125 x = 53.078311125 Simplifying x = 53.078311125Subproblem 2
x + -27.5 = -25.578311125 Simplifying x + -27.5 = -25.578311125 Reorder the terms: -27.5 + x = -25.578311125 Solving -27.5 + x = -25.578311125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -25.578311125 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -25.578311125 + 27.5 x = -25.578311125 + 27.5 Combine like terms: -25.578311125 + 27.5 = 1.921688875 x = 1.921688875 Simplifying x = 1.921688875Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.078311125, 1.921688875}Solution
x = {53.078311125, 1.921688875}
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