(x+18)(x+36)=1260

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Solution for (x+18)(x+36)=1260 equation:


Simplifying
(x + 18)(x + 36) = 1260

Reorder the terms:
(18 + x)(x + 36) = 1260

Reorder the terms:
(18 + x)(36 + x) = 1260

Multiply (18 + x) * (36 + x)
(18(36 + x) + x(36 + x)) = 1260
((36 * 18 + x * 18) + x(36 + x)) = 1260
((648 + 18x) + x(36 + x)) = 1260
(648 + 18x + (36 * x + x * x)) = 1260
(648 + 18x + (36x + x2)) = 1260

Combine like terms: 18x + 36x = 54x
(648 + 54x + x2) = 1260

Solving
648 + 54x + x2 = 1260

Solving for variable 'x'.

Reorder the terms:
648 + -1260 + 54x + x2 = 1260 + -1260

Combine like terms: 648 + -1260 = -612
-612 + 54x + x2 = 1260 + -1260

Combine like terms: 1260 + -1260 = 0
-612 + 54x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '612' to each side of the equation.
-612 + 54x + 612 + x2 = 0 + 612

Reorder the terms:
-612 + 612 + 54x + x2 = 0 + 612

Combine like terms: -612 + 612 = 0
0 + 54x + x2 = 0 + 612
54x + x2 = 0 + 612

Combine like terms: 0 + 612 = 612
54x + x2 = 612

The x term is 54x.  Take half its coefficient (27).
Square it (729) and add it to both sides.

Add '729' to each side of the equation.
54x + 729 + x2 = 612 + 729

Reorder the terms:
729 + 54x + x2 = 612 + 729

Combine like terms: 612 + 729 = 1341
729 + 54x + x2 = 1341

Factor a perfect square on the left side:
(x + 27)(x + 27) = 1341

Calculate the square root of the right side: 36.619666847

Break this problem into two subproblems by setting 
(x + 27) equal to 36.619666847 and -36.619666847.

Subproblem 1

x + 27 = 36.619666847 Simplifying x + 27 = 36.619666847 Reorder the terms: 27 + x = 36.619666847 Solving 27 + x = 36.619666847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 36.619666847 + -27 Combine like terms: 27 + -27 = 0 0 + x = 36.619666847 + -27 x = 36.619666847 + -27 Combine like terms: 36.619666847 + -27 = 9.619666847 x = 9.619666847 Simplifying x = 9.619666847

Subproblem 2

x + 27 = -36.619666847 Simplifying x + 27 = -36.619666847 Reorder the terms: 27 + x = -36.619666847 Solving 27 + x = -36.619666847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = -36.619666847 + -27 Combine like terms: 27 + -27 = 0 0 + x = -36.619666847 + -27 x = -36.619666847 + -27 Combine like terms: -36.619666847 + -27 = -63.619666847 x = -63.619666847 Simplifying x = -63.619666847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.619666847, -63.619666847}

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