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Simplifying (x + 18)(x + 14) = 504 Reorder the terms: (18 + x)(x + 14) = 504 Reorder the terms: (18 + x)(14 + x) = 504 Multiply (18 + x) * (14 + x) (18(14 + x) + x(14 + x)) = 504 ((14 * 18 + x * 18) + x(14 + x)) = 504 ((252 + 18x) + x(14 + x)) = 504 (252 + 18x + (14 * x + x * x)) = 504 (252 + 18x + (14x + x2)) = 504 Combine like terms: 18x + 14x = 32x (252 + 32x + x2) = 504 Solving 252 + 32x + x2 = 504 Solving for variable 'x'. Reorder the terms: 252 + -504 + 32x + x2 = 504 + -504 Combine like terms: 252 + -504 = -252 -252 + 32x + x2 = 504 + -504 Combine like terms: 504 + -504 = 0 -252 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '252' to each side of the equation. -252 + 32x + 252 + x2 = 0 + 252 Reorder the terms: -252 + 252 + 32x + x2 = 0 + 252 Combine like terms: -252 + 252 = 0 0 + 32x + x2 = 0 + 252 32x + x2 = 0 + 252 Combine like terms: 0 + 252 = 252 32x + x2 = 252 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 252 + 256 Reorder the terms: 256 + 32x + x2 = 252 + 256 Combine like terms: 252 + 256 = 508 256 + 32x + x2 = 508 Factor a perfect square on the left side: (x + 16)(x + 16) = 508 Calculate the square root of the right side: 22.538855339 Break this problem into two subproblems by setting (x + 16) equal to 22.538855339 and -22.538855339.Subproblem 1
x + 16 = 22.538855339 Simplifying x + 16 = 22.538855339 Reorder the terms: 16 + x = 22.538855339 Solving 16 + x = 22.538855339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 22.538855339 + -16 Combine like terms: 16 + -16 = 0 0 + x = 22.538855339 + -16 x = 22.538855339 + -16 Combine like terms: 22.538855339 + -16 = 6.538855339 x = 6.538855339 Simplifying x = 6.538855339Subproblem 2
x + 16 = -22.538855339 Simplifying x + 16 = -22.538855339 Reorder the terms: 16 + x = -22.538855339 Solving 16 + x = -22.538855339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -22.538855339 + -16 Combine like terms: 16 + -16 = 0 0 + x = -22.538855339 + -16 x = -22.538855339 + -16 Combine like terms: -22.538855339 + -16 = -38.538855339 x = -38.538855339 Simplifying x = -38.538855339Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.538855339, -38.538855339}
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