(12+2x)(24+2x)=252

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Solution for (12+2x)(24+2x)=252 equation:


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 = -0.514718626

Subproblem 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 = -17.485281374

Solution

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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