x^2+4x=41

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Solution for x^2+4x=41 equation:


Simplifying
x2 + 4x = 41

Reorder the terms:
4x + x2 = 41

Solving
4x + x2 = 41

Solving for variable 'x'.

Reorder the terms:
-41 + 4x + x2 = 41 + -41

Combine like terms: 41 + -41 = 0
-41 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 4x + 41 + x2 = 0 + 41

Reorder the terms:
-41 + 41 + 4x + x2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 4x + x2 = 0 + 41
4x + x2 = 0 + 41

Combine like terms: 0 + 41 = 41
4x + x2 = 41

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 = 41 + 4

Reorder the terms:
4 + 4x + x2 = 41 + 4

Combine like terms: 41 + 4 = 45
4 + 4x + x2 = 45

Factor a perfect square on the left side:
(x + 2)(x + 2) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 2) equal to 6.708203933 and -6.708203933.

Subproblem 1

x + 2 = 6.708203933 Simplifying x + 2 = 6.708203933 Reorder the terms: 2 + x = 6.708203933 Solving 2 + x = 6.708203933 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 = 6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.708203933 + -2 x = 6.708203933 + -2 Combine like terms: 6.708203933 + -2 = 4.708203933 x = 4.708203933 Simplifying x = 4.708203933

Subproblem 2

x + 2 = -6.708203933 Simplifying x + 2 = -6.708203933 Reorder the terms: 2 + x = -6.708203933 Solving 2 + x = -6.708203933 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 = -6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.708203933 + -2 x = -6.708203933 + -2 Combine like terms: -6.708203933 + -2 = -8.708203933 x = -8.708203933 Simplifying x = -8.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.708203933, -8.708203933}

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