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Simplifying (12 + 2x)(12 + 2x) = 396 Multiply (12 + 2x) * (12 + 2x) (12(12 + 2x) + 2x * (12 + 2x)) = 396 ((12 * 12 + 2x * 12) + 2x * (12 + 2x)) = 396 ((144 + 24x) + 2x * (12 + 2x)) = 396 (144 + 24x + (12 * 2x + 2x * 2x)) = 396 (144 + 24x + (24x + 4x2)) = 396 Combine like terms: 24x + 24x = 48x (144 + 48x + 4x2) = 396 Solving 144 + 48x + 4x2 = 396 Solving for variable 'x'. Reorder the terms: 144 + -396 + 48x + 4x2 = 396 + -396 Combine like terms: 144 + -396 = -252 -252 + 48x + 4x2 = 396 + -396 Combine like terms: 396 + -396 = 0 -252 + 48x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-63 + 12x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-63 + 12x + x2)' equal to zero and attempt to solve: Simplifying -63 + 12x + x2 = 0 Solving -63 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 12x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 12x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 12x + x2 = 0 + 63 12x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 12x + x2 = 63 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 63 + 36 Reorder the terms: 36 + 12x + x2 = 63 + 36 Combine like terms: 63 + 36 = 99 36 + 12x + x2 = 99 Factor a perfect square on the left side: (x + 6)(x + 6) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + 6) equal to 9.949874371 and -9.949874371.Subproblem 1
x + 6 = 9.949874371 Simplifying x + 6 = 9.949874371 Reorder the terms: 6 + x = 9.949874371 Solving 6 + x = 9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 9.949874371 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.949874371 + -6 x = 9.949874371 + -6 Combine like terms: 9.949874371 + -6 = 3.949874371 x = 3.949874371 Simplifying x = 3.949874371Subproblem 2
x + 6 = -9.949874371 Simplifying x + 6 = -9.949874371 Reorder the terms: 6 + x = -9.949874371 Solving 6 + x = -9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -9.949874371 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.949874371 + -6 x = -9.949874371 + -6 Combine like terms: -9.949874371 + -6 = -15.949874371 x = -15.949874371 Simplifying x = -15.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.949874371, -15.949874371}Solution
x = {3.949874371, -15.949874371}
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