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Simplifying (2x + 2)(2x + 2) = 168 Reorder the terms: (2 + 2x)(2x + 2) = 168 Reorder the terms: (2 + 2x)(2 + 2x) = 168 Multiply (2 + 2x) * (2 + 2x) (2(2 + 2x) + 2x * (2 + 2x)) = 168 ((2 * 2 + 2x * 2) + 2x * (2 + 2x)) = 168 ((4 + 4x) + 2x * (2 + 2x)) = 168 (4 + 4x + (2 * 2x + 2x * 2x)) = 168 (4 + 4x + (4x + 4x2)) = 168 Combine like terms: 4x + 4x = 8x (4 + 8x + 4x2) = 168 Solving 4 + 8x + 4x2 = 168 Solving for variable 'x'. Reorder the terms: 4 + -168 + 8x + 4x2 = 168 + -168 Combine like terms: 4 + -168 = -164 -164 + 8x + 4x2 = 168 + -168 Combine like terms: 168 + -168 = 0 -164 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-41 + 2x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-41 + 2x + x2)' equal to zero and attempt to solve: Simplifying -41 + 2x + x2 = 0 Solving -41 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 2x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 2x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 2x + x2 = 0 + 41 2x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 2x + x2 = 41 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 = 41 + 1 Reorder the terms: 1 + 2x + x2 = 41 + 1 Combine like terms: 41 + 1 = 42 1 + 2x + x2 = 42 Factor a perfect square on the left side: (x + 1)(x + 1) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + 1) equal to 6.480740698 and -6.480740698.Subproblem 1
x + 1 = 6.480740698 Simplifying x + 1 = 6.480740698 Reorder the terms: 1 + x = 6.480740698 Solving 1 + x = 6.480740698 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 = 6.480740698 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.480740698 + -1 x = 6.480740698 + -1 Combine like terms: 6.480740698 + -1 = 5.480740698 x = 5.480740698 Simplifying x = 5.480740698Subproblem 2
x + 1 = -6.480740698 Simplifying x + 1 = -6.480740698 Reorder the terms: 1 + x = -6.480740698 Solving 1 + x = -6.480740698 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 = -6.480740698 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.480740698 + -1 x = -6.480740698 + -1 Combine like terms: -6.480740698 + -1 = -7.480740698 x = -7.480740698 Simplifying x = -7.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.480740698, -7.480740698}Solution
x = {5.480740698, -7.480740698}
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