(x*x)+4x=11

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Solution for (x*x)+4x=11 equation: 


Simplifying
(x * x) + 4x = 11

Multiply x * x
(x2) + 4x = 11
x2 + 4x = 11

Reorder the terms:
4x + x2 = 11

Solving
4x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + 4x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 4x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 4x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4x + x2 = 0 + 11
4x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
4x + x2 = 11

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 = 11 + 4

Reorder the terms:
4 + 4x + x2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + 4x + x2 = 15

Factor a perfect square on the left side:
(x + 2)(x + 2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 2) equal to 3.872983346 and -3.872983346.


Subproblem 1
x + 2 = 3.872983346

Simplifying
x + 2 = 3.872983346

Reorder the terms:
2 + x = 3.872983346

Solving
2 + x = 3.872983346

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 = 3.872983346 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.872983346 + -2
x = 3.872983346 + -2

Combine like terms: 3.872983346 + -2 = 1.872983346
x = 1.872983346

Simplifying
x = 1.872983346


Subproblem 2
x + 2 = -3.872983346

Simplifying
x + 2 = -3.872983346

Reorder the terms:
2 + x = -3.872983346

Solving
2 + x = -3.872983346

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 = -3.872983346 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.872983346 + -2
x = -3.872983346 + -2

Combine like terms: -3.872983346 + -2 = -5.872983346
x = -5.872983346

Simplifying
x = -5.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.872983346, -5.872983346}

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