x(x+18)=26(26+16)

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Solution for x(x+18)=26(26+16) equation:


Simplifying
x(x + 18) = 26(26 + 16)

Reorder the terms:
x(18 + x) = 26(26 + 16)
(18 * x + x * x) = 26(26 + 16)
(18x + x2) = 26(26 + 16)

Combine like terms: 26 + 16 = 42
18x + x2 = 26(42)

Multiply 26 * 42
18x + x2 = 1092

Solving
18x + x2 = 1092

Solving for variable 'x'.

Reorder the terms:
-1092 + 18x + x2 = 1092 + -1092

Combine like terms: 1092 + -1092 = 0
-1092 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1092' to each side of the equation.
-1092 + 18x + 1092 + x2 = 0 + 1092

Reorder the terms:
-1092 + 1092 + 18x + x2 = 0 + 1092

Combine like terms: -1092 + 1092 = 0
0 + 18x + x2 = 0 + 1092
18x + x2 = 0 + 1092

Combine like terms: 0 + 1092 = 1092
18x + x2 = 1092

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 = 1092 + 81

Reorder the terms:
81 + 18x + x2 = 1092 + 81

Combine like terms: 1092 + 81 = 1173
81 + 18x + x2 = 1173

Factor a perfect square on the left side:
(x + 9)(x + 9) = 1173

Calculate the square root of the right side: 34.249087579

Break this problem into two subproblems by setting 
(x + 9) equal to 34.249087579 and -34.249087579.

Subproblem 1

x + 9 = 34.249087579 Simplifying x + 9 = 34.249087579 Reorder the terms: 9 + x = 34.249087579 Solving 9 + x = 34.249087579 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 = 34.249087579 + -9 Combine like terms: 9 + -9 = 0 0 + x = 34.249087579 + -9 x = 34.249087579 + -9 Combine like terms: 34.249087579 + -9 = 25.249087579 x = 25.249087579 Simplifying x = 25.249087579

Subproblem 2

x + 9 = -34.249087579 Simplifying x + 9 = -34.249087579 Reorder the terms: 9 + x = -34.249087579 Solving 9 + x = -34.249087579 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 = -34.249087579 + -9 Combine like terms: 9 + -9 = 0 0 + x = -34.249087579 + -9 x = -34.249087579 + -9 Combine like terms: -34.249087579 + -9 = -43.249087579 x = -43.249087579 Simplifying x = -43.249087579

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.249087579, -43.249087579}

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