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Simplifying 2x2 + 4x = 266 Reorder the terms: 4x + 2x2 = 266 Solving 4x + 2x2 = 266 Solving for variable 'x'. Reorder the terms: -266 + 4x + 2x2 = 266 + -266 Combine like terms: 266 + -266 = 0 -266 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-133 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-133 + 2x + x2)' equal to zero and attempt to solve: Simplifying -133 + 2x + x2 = 0 Solving -133 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '133' to each side of the equation. -133 + 2x + 133 + x2 = 0 + 133 Reorder the terms: -133 + 133 + 2x + x2 = 0 + 133 Combine like terms: -133 + 133 = 0 0 + 2x + x2 = 0 + 133 2x + x2 = 0 + 133 Combine like terms: 0 + 133 = 133 2x + x2 = 133 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 133 + 1 Reorder the terms: 1 + 2x + x2 = 133 + 1 Combine like terms: 133 + 1 = 134 1 + 2x + x2 = 134 Factor a perfect square on the left side: (x + 1)(x + 1) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + 1) equal to 11.575836903 and -11.575836903.Subproblem 1
x + 1 = 11.575836903 Simplifying x + 1 = 11.575836903 Reorder the terms: 1 + x = 11.575836903 Solving 1 + x = 11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 11.575836903 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.575836903 + -1 x = 11.575836903 + -1 Combine like terms: 11.575836903 + -1 = 10.575836903 x = 10.575836903 Simplifying x = 10.575836903Subproblem 2
x + 1 = -11.575836903 Simplifying x + 1 = -11.575836903 Reorder the terms: 1 + x = -11.575836903 Solving 1 + x = -11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -11.575836903 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.575836903 + -1 x = -11.575836903 + -1 Combine like terms: -11.575836903 + -1 = -12.575836903 x = -12.575836903 Simplifying x = -12.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.575836903, -12.575836903}Solution
x = {10.575836903, -12.575836903}
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