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Simplifying 2x(x + x + 12) = 92 Reorder the terms: 2x(12 + x + x) = 92 Combine like terms: x + x = 2x 2x(12 + 2x) = 92 (12 * 2x + 2x * 2x) = 92 (24x + 4x2) = 92 Solving 24x + 4x2 = 92 Solving for variable 'x'. Reorder the terms: -92 + 24x + 4x2 = 92 + -92 Combine like terms: 92 + -92 = 0 -92 + 24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-23 + 6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-23 + 6x + x2)' equal to zero and attempt to solve: Simplifying -23 + 6x + x2 = 0 Solving -23 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 6x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 6x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 6x + x2 = 0 + 23 6x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 6x + x2 = 23 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 23 + 9 Reorder the terms: 9 + 6x + x2 = 23 + 9 Combine like terms: 23 + 9 = 32 9 + 6x + x2 = 32 Factor a perfect square on the left side: (x + 3)(x + 3) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 3) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 3 = 5.656854249 Simplifying x + 3 = 5.656854249 Reorder the terms: 3 + x = 5.656854249 Solving 3 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.656854249 + -3 x = 5.656854249 + -3 Combine like terms: 5.656854249 + -3 = 2.656854249 x = 2.656854249 Simplifying x = 2.656854249Subproblem 2
x + 3 = -5.656854249 Simplifying x + 3 = -5.656854249 Reorder the terms: 3 + x = -5.656854249 Solving 3 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.656854249 + -3 x = -5.656854249 + -3 Combine like terms: -5.656854249 + -3 = -8.656854249 x = -8.656854249 Simplifying x = -8.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.656854249, -8.656854249}Solution
x = {2.656854249, -8.656854249}
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