7x+5x(x+3)+4x+x+2=

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Solution for 7x+5x(x+3)+4x+x+2= equation: 


Simplifying
7x + 5x(x + 3) + 4x + x + 2 = 0

Reorder the terms:
7x + 5x(3 + x) + 4x + x + 2 = 0
7x + (3 * 5x + x * 5x) + 4x + x + 2 = 0
7x + (15x + 5x2) + 4x + x + 2 = 0

Reorder the terms:
2 + 7x + 15x + 4x + x + 5x2 = 0

Combine like terms: 7x + 15x = 22x
2 + 22x + 4x + x + 5x2 = 0

Combine like terms: 22x + 4x = 26x
2 + 26x + x + 5x2 = 0

Combine like terms: 26x + x = 27x
2 + 27x + 5x2 = 0

Solving
2 + 27x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.4 + 5.4x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 5.4x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 5.4x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 5.4x + x2 = 0 + -0.4
5.4x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
5.4x + x2 = -0.4

The x term is 5.4x.  Take half its coefficient (2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
5.4x + 7.29 + x2 = -0.4 + 7.29

Reorder the terms:
7.29 + 5.4x + x2 = -0.4 + 7.29

Combine like terms: -0.4 + 7.29 = 6.89
7.29 + 5.4x + x2 = 6.89

Factor a perfect square on the left side:
(x + 2.7)(x + 2.7) = 6.89

Calculate the square root of the right side: 2.62488095

Break this problem into two subproblems by setting 
(x + 2.7) equal to 2.62488095 and -2.62488095.


Subproblem 1
x + 2.7 = 2.62488095

Simplifying
x + 2.7 = 2.62488095

Reorder the terms:
2.7 + x = 2.62488095

Solving
2.7 + x = 2.62488095

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.7' to each side of the equation.
2.7 + -2.7 + x = 2.62488095 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + x = 2.62488095 + -2.7
x = 2.62488095 + -2.7

Combine like terms: 2.62488095 + -2.7 = -0.07511905
x = -0.07511905

Simplifying
x = -0.07511905


Subproblem 2
x + 2.7 = -2.62488095

Simplifying
x + 2.7 = -2.62488095

Reorder the terms:
2.7 + x = -2.62488095

Solving
2.7 + x = -2.62488095

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.7' to each side of the equation.
2.7 + -2.7 + x = -2.62488095 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + x = -2.62488095 + -2.7
x = -2.62488095 + -2.7

Combine like terms: -2.62488095 + -2.7 = -5.32488095
x = -5.32488095

Simplifying
x = -5.32488095


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.07511905, -5.32488095}

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