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Simplifying (12 + 2x)(24 + 2x) = 252 Multiply (12 + 2x) * (24 + 2x) (12(24 + 2x) + 2x * (24 + 2x)) = 252 ((24 * 12 + 2x * 12) + 2x * (24 + 2x)) = 252 ((288 + 24x) + 2x * (24 + 2x)) = 252 (288 + 24x + (24 * 2x + 2x * 2x)) = 252 (288 + 24x + (48x + 4x2)) = 252 Combine like terms: 24x + 48x = 72x (288 + 72x + 4x2) = 252 Solving 288 + 72x + 4x2 = 252 Solving for variable 'x'. Reorder the terms: 288 + -252 + 72x + 4x2 = 252 + -252 Combine like terms: 288 + -252 = 36 36 + 72x + 4x2 = 252 + -252 Combine like terms: 252 + -252 = 0 36 + 72x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + 18x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + 18x + x2)' equal to zero and attempt to solve: Simplifying 9 + 18x + x2 = 0 Solving 9 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 18x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 18x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 18x + x2 = 0 + -9 18x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 18x + x2 = -9 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -9 + 81 Reorder the terms: 81 + 18x + x2 = -9 + 81 Combine like terms: -9 + 81 = 72 81 + 18x + x2 = 72 Factor a perfect square on the left side: (x + 9)(x + 9) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + 9) equal to 8.485281374 and -8.485281374.Subproblem 1
x + 9 = 8.485281374 Simplifying x + 9 = 8.485281374 Reorder the terms: 9 + x = 8.485281374 Solving 9 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 8.485281374 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.485281374 + -9 x = 8.485281374 + -9 Combine like terms: 8.485281374 + -9 = -0.514718626 x = -0.514718626 Simplifying x = -0.514718626Subproblem 2
x + 9 = -8.485281374 Simplifying x + 9 = -8.485281374 Reorder the terms: 9 + x = -8.485281374 Solving 9 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -8.485281374 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.485281374 + -9 x = -8.485281374 + -9 Combine like terms: -8.485281374 + -9 = -17.485281374 x = -17.485281374 Simplifying x = -17.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.514718626, -17.485281374}Solution
x = {-0.514718626, -17.485281374}
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