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Simplifying (7 + 2x)(2 + 2x) = 504 Multiply (7 + 2x) * (2 + 2x) (7(2 + 2x) + 2x * (2 + 2x)) = 504 ((2 * 7 + 2x * 7) + 2x * (2 + 2x)) = 504 ((14 + 14x) + 2x * (2 + 2x)) = 504 (14 + 14x + (2 * 2x + 2x * 2x)) = 504 (14 + 14x + (4x + 4x2)) = 504 Combine like terms: 14x + 4x = 18x (14 + 18x + 4x2) = 504 Solving 14 + 18x + 4x2 = 504 Solving for variable 'x'. Reorder the terms: 14 + -504 + 18x + 4x2 = 504 + -504 Combine like terms: 14 + -504 = -490 -490 + 18x + 4x2 = 504 + -504 Combine like terms: 504 + -504 = 0 -490 + 18x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-245 + 9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-245 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -245 + 9x + 2x2 = 0 Solving -245 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -122.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '122.5' to each side of the equation. -122.5 + 4.5x + 122.5 + x2 = 0 + 122.5 Reorder the terms: -122.5 + 122.5 + 4.5x + x2 = 0 + 122.5 Combine like terms: -122.5 + 122.5 = 0.0 0.0 + 4.5x + x2 = 0 + 122.5 4.5x + x2 = 0 + 122.5 Combine like terms: 0 + 122.5 = 122.5 4.5x + x2 = 122.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 122.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 122.5 + 5.0625 Combine like terms: 122.5 + 5.0625 = 127.5625 5.0625 + 4.5x + x2 = 127.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 127.5625 Calculate the square root of the right side: 11.294356998 Break this problem into two subproblems by setting (x + 2.25) equal to 11.294356998 and -11.294356998.Subproblem 1
x + 2.25 = 11.294356998 Simplifying x + 2.25 = 11.294356998 Reorder the terms: 2.25 + x = 11.294356998 Solving 2.25 + x = 11.294356998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 11.294356998 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 11.294356998 + -2.25 x = 11.294356998 + -2.25 Combine like terms: 11.294356998 + -2.25 = 9.044356998 x = 9.044356998 Simplifying x = 9.044356998Subproblem 2
x + 2.25 = -11.294356998 Simplifying x + 2.25 = -11.294356998 Reorder the terms: 2.25 + x = -11.294356998 Solving 2.25 + x = -11.294356998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -11.294356998 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -11.294356998 + -2.25 x = -11.294356998 + -2.25 Combine like terms: -11.294356998 + -2.25 = -13.544356998 x = -13.544356998 Simplifying x = -13.544356998Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.044356998, -13.544356998}Solution
x = {9.044356998, -13.544356998}
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