9x^2+36x=41

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Solution for 9x^2+36x=41 equation:


Simplifying
9x2 + 36x = 41

Reorder the terms:
36x + 9x2 = 41

Solving
36x + 9x2 = 41

Solving for variable 'x'.

Reorder the terms:
-41 + 36x + 9x2 = 41 + -41

Combine like terms: 41 + -41 = 0
-41 + 36x + 9x2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-4.555555556 + 4x + x2 = 0

Move the constant term to the right:

Add '4.555555556' to each side of the equation.
-4.555555556 + 4x + 4.555555556 + x2 = 0 + 4.555555556

Reorder the terms:
-4.555555556 + 4.555555556 + 4x + x2 = 0 + 4.555555556

Combine like terms: -4.555555556 + 4.555555556 = 0.000000000
0.000000000 + 4x + x2 = 0 + 4.555555556
4x + x2 = 0 + 4.555555556

Combine like terms: 0 + 4.555555556 = 4.555555556
4x + x2 = 4.555555556

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 4.555555556 + 4

Reorder the terms:
4 + 4x + x2 = 4.555555556 + 4

Combine like terms: 4.555555556 + 4 = 8.555555556
4 + 4x + x2 = 8.555555556

Factor a perfect square on the left side:
(x + 2)(x + 2) = 8.555555556

Calculate the square root of the right side: 2.924988129

Break this problem into two subproblems by setting 
(x + 2) equal to 2.924988129 and -2.924988129.

Subproblem 1

x + 2 = 2.924988129 Simplifying x + 2 = 2.924988129 Reorder the terms: 2 + x = 2.924988129 Solving 2 + x = 2.924988129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.924988129 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.924988129 + -2 x = 2.924988129 + -2 Combine like terms: 2.924988129 + -2 = 0.924988129 x = 0.924988129 Simplifying x = 0.924988129

Subproblem 2

x + 2 = -2.924988129 Simplifying x + 2 = -2.924988129 Reorder the terms: 2 + x = -2.924988129 Solving 2 + x = -2.924988129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.924988129 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.924988129 + -2 x = -2.924988129 + -2 Combine like terms: -2.924988129 + -2 = -4.924988129 x = -4.924988129 Simplifying x = -4.924988129

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.924988129, -4.924988129}

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