x(x+36)=5125

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Solution for x(x+36)=5125 equation:


Simplifying
x(x + 36) = 5125

Reorder the terms:
x(36 + x) = 5125
(36 * x + x * x) = 5125
(36x + x2) = 5125

Solving
36x + x2 = 5125

Solving for variable 'x'.

Reorder the terms:
-5125 + 36x + x2 = 5125 + -5125

Combine like terms: 5125 + -5125 = 0
-5125 + 36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5125' to each side of the equation.
-5125 + 36x + 5125 + x2 = 0 + 5125

Reorder the terms:
-5125 + 5125 + 36x + x2 = 0 + 5125

Combine like terms: -5125 + 5125 = 0
0 + 36x + x2 = 0 + 5125
36x + x2 = 0 + 5125

Combine like terms: 0 + 5125 = 5125
36x + x2 = 5125

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = 5125 + 324

Reorder the terms:
324 + 36x + x2 = 5125 + 324

Combine like terms: 5125 + 324 = 5449
324 + 36x + x2 = 5449

Factor a perfect square on the left side:
(x + 18)(x + 18) = 5449

Calculate the square root of the right side: 73.817342136

Break this problem into two subproblems by setting 
(x + 18) equal to 73.817342136 and -73.817342136.

Subproblem 1

x + 18 = 73.817342136 Simplifying x + 18 = 73.817342136 Reorder the terms: 18 + x = 73.817342136 Solving 18 + x = 73.817342136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 73.817342136 + -18 Combine like terms: 18 + -18 = 0 0 + x = 73.817342136 + -18 x = 73.817342136 + -18 Combine like terms: 73.817342136 + -18 = 55.817342136 x = 55.817342136 Simplifying x = 55.817342136

Subproblem 2

x + 18 = -73.817342136 Simplifying x + 18 = -73.817342136 Reorder the terms: 18 + x = -73.817342136 Solving 18 + x = -73.817342136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -73.817342136 + -18 Combine like terms: 18 + -18 = 0 0 + x = -73.817342136 + -18 x = -73.817342136 + -18 Combine like terms: -73.817342136 + -18 = -91.817342136 x = -91.817342136 Simplifying x = -91.817342136

Solution

The solution to the problem is based on the solutions from the subproblems. x = {55.817342136, -91.817342136}

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