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Simplifying 2x2 + 4x + -6 = 236 Reorder the terms: -6 + 4x + 2x2 = 236 Solving -6 + 4x + 2x2 = 236 Solving for variable 'x'. Reorder the terms: -6 + -236 + 4x + 2x2 = 236 + -236 Combine like terms: -6 + -236 = -242 -242 + 4x + 2x2 = 236 + -236 Combine like terms: 236 + -236 = 0 -242 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-121 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-121 + 2x + x2)' equal to zero and attempt to solve: Simplifying -121 + 2x + x2 = 0 Solving -121 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + 2x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + 2x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 2x + x2 = 0 + 121 2x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 2x + x2 = 121 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 = 121 + 1 Reorder the terms: 1 + 2x + x2 = 121 + 1 Combine like terms: 121 + 1 = 122 1 + 2x + x2 = 122 Factor a perfect square on the left side: (x + 1)(x + 1) = 122 Calculate the square root of the right side: 11.045361017 Break this problem into two subproblems by setting (x + 1) equal to 11.045361017 and -11.045361017.Subproblem 1
x + 1 = 11.045361017 Simplifying x + 1 = 11.045361017 Reorder the terms: 1 + x = 11.045361017 Solving 1 + x = 11.045361017 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 = 11.045361017 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.045361017 + -1 x = 11.045361017 + -1 Combine like terms: 11.045361017 + -1 = 10.045361017 x = 10.045361017 Simplifying x = 10.045361017Subproblem 2
x + 1 = -11.045361017 Simplifying x + 1 = -11.045361017 Reorder the terms: 1 + x = -11.045361017 Solving 1 + x = -11.045361017 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 = -11.045361017 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.045361017 + -1 x = -11.045361017 + -1 Combine like terms: -11.045361017 + -1 = -12.045361017 x = -12.045361017 Simplifying x = -12.045361017Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.045361017, -12.045361017}Solution
x = {10.045361017, -12.045361017}
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