x*x+7x+10+5x=

Solution for x*x+7x+10+5x= equation:

Simplifying
x * x + 7x + 10 + 5x = 0

Multiply x * x
x2 + 7x + 10 + 5x = 0

Reorder the terms:
10 + 7x + 5x + x2 = 0

Combine like terms: 7x + 5x = 12x
10 + 12x + x2 = 0

Solving
10 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 12x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 12x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 12x + x2 = 0 + -10
12x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
12x + x2 = -10

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -10 + 36

Reorder the terms:
36 + 12x + x2 = -10 + 36

Combine like terms: -10 + 36 = 26
36 + 12x + x2 = 26

Factor a perfect square on the left side:
(x + 6)(x + 6) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + 6) equal to 5.099019514 and -5.099019514.

Subproblem 1
x + 6 = 5.099019514

Simplifying
x + 6 = 5.099019514

Reorder the terms:
6 + x = 5.099019514

Solving
6 + x = 5.099019514

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 5.099019514 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.099019514 + -6
x = 5.099019514 + -6

Combine like terms: 5.099019514 + -6 = -0.900980486
x = -0.900980486

Simplifying
x = -0.900980486

Subproblem 2
x + 6 = -5.099019514

Simplifying
x + 6 = -5.099019514

Reorder the terms:
6 + x = -5.099019514

Solving
6 + x = -5.099019514

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -5.099019514 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.099019514 + -6
x = -5.099019514 + -6

Combine like terms: -5.099019514 + -6 = -11.099019514
x = -11.099019514

Simplifying
x = -11.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.900980486, -11.099019514}