x^2+4x+0.24=0

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Solution for x^2+4x+0.24=0 equation: 


Simplifying
x2 + 4x + 0.24 = 0

Reorder the terms:
0.24 + 4x + x2 = 0

Solving
0.24 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.24' to each side of the equation.
0.24 + 4x + -0.24 + x2 = 0 + -0.24

Reorder the terms:
0.24 + -0.24 + 4x + x2 = 0 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + 4x + x2 = 0 + -0.24
4x + x2 = 0 + -0.24

Combine like terms: 0 + -0.24 = -0.24
4x + x2 = -0.24

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 = -0.24 + 4

Reorder the terms:
4 + 4x + x2 = -0.24 + 4

Combine like terms: -0.24 + 4 = 3.76
4 + 4x + x2 = 3.76

Factor a perfect square on the left side:
(x + 2)(x + 2) = 3.76

Calculate the square root of the right side: 1.939071943

Break this problem into two subproblems by setting 
(x + 2) equal to 1.939071943 and -1.939071943.


Subproblem 1
x + 2 = 1.939071943

Simplifying
x + 2 = 1.939071943

Reorder the terms:
2 + x = 1.939071943

Solving
2 + x = 1.939071943

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 = 1.939071943 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.939071943 + -2
x = 1.939071943 + -2

Combine like terms: 1.939071943 + -2 = -0.060928057
x = -0.060928057

Simplifying
x = -0.060928057


Subproblem 2
x + 2 = -1.939071943

Simplifying
x + 2 = -1.939071943

Reorder the terms:
2 + x = -1.939071943

Solving
2 + x = -1.939071943

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 = -1.939071943 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.939071943 + -2
x = -1.939071943 + -2

Combine like terms: -1.939071943 + -2 = -3.939071943
x = -3.939071943

Simplifying
x = -3.939071943


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.060928057, -3.939071943}

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