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Simplifying (2x + 4)(x) = 122 Reorder the terms: (4 + 2x)(x) = 122 Reorder the terms for easier multiplication: x(4 + 2x) = 122 (4 * x + 2x * x) = 122 (4x + 2x2) = 122 Solving 4x + 2x2 = 122 Solving for variable 'x'. Reorder the terms: -122 + 4x + 2x2 = 122 + -122 Combine like terms: 122 + -122 = 0 -122 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-61 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-61 + 2x + x2)' equal to zero and attempt to solve: Simplifying -61 + 2x + x2 = 0 Solving -61 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 2x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 2x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 2x + x2 = 0 + 61 2x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 2x + x2 = 61 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 = 61 + 1 Reorder the terms: 1 + 2x + x2 = 61 + 1 Combine like terms: 61 + 1 = 62 1 + 2x + x2 = 62 Factor a perfect square on the left side: (x + 1)(x + 1) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + 1) equal to 7.874007874 and -7.874007874.Subproblem 1
x + 1 = 7.874007874 Simplifying x + 1 = 7.874007874 Reorder the terms: 1 + x = 7.874007874 Solving 1 + x = 7.874007874 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 = 7.874007874 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.874007874 + -1 x = 7.874007874 + -1 Combine like terms: 7.874007874 + -1 = 6.874007874 x = 6.874007874 Simplifying x = 6.874007874Subproblem 2
x + 1 = -7.874007874 Simplifying x + 1 = -7.874007874 Reorder the terms: 1 + x = -7.874007874 Solving 1 + x = -7.874007874 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 = -7.874007874 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.874007874 + -1 x = -7.874007874 + -1 Combine like terms: -7.874007874 + -1 = -8.874007874 x = -8.874007874 Simplifying x = -8.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.874007874, -8.874007874}Solution
x = {6.874007874, -8.874007874}
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