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

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

Simplifying
0 = (5x2 + -1x + -7) + (2x2 + 3x + 4)

Reorder the terms:
0 = (-7 + -1x + 5x2) + (2x2 + 3x + 4)

Remove parenthesis around (-7 + -1x + 5x2)
0 = -7 + -1x + 5x2 + (2x2 + 3x + 4)

Reorder the terms:
0 = -7 + -1x + 5x2 + (4 + 3x + 2x2)

Remove parenthesis around (4 + 3x + 2x2)
0 = -7 + -1x + 5x2 + 4 + 3x + 2x2

Reorder the terms:
0 = -7 + 4 + -1x + 3x + 5x2 + 2x2

Combine like terms: -7 + 4 = -3
0 = -3 + -1x + 3x + 5x2 + 2x2

Combine like terms: -1x + 3x = 2x
0 = -3 + 2x + 5x2 + 2x2

Combine like terms: 5x2 + 2x2 = 7x2
0 = -3 + 2x + 7x2

Solving
0 = -3 + 2x + 7x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -2x + -7x2 = -3 + 2x + 7x2 + 3 + -2x + -7x2

Reorder the terms:
3 + -2x + -7x2 = -3 + 3 + 2x + -2x + 7x2 + -7x2

Combine like terms: -3 + 3 = 0
3 + -2x + -7x2 = 0 + 2x + -2x + 7x2 + -7x2
3 + -2x + -7x2 = 2x + -2x + 7x2 + -7x2

Combine like terms: 2x + -2x = 0
3 + -2x + -7x2 = 0 + 7x2 + -7x2
3 + -2x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
3 + -2x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.4285714286 + 0.2857142857x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.2857142857x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + 0.2857142857x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + 0.2857142857x + x2 = 0 + 0.4285714286
0.2857142857x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
0.2857142857x + x2 = 0.4285714286

The x term is 0.2857142857x.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857x + 0.02040816328 + x2 = 0.4285714286 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x + x2 = 0.4285714286 + 0.02040816328

Combine like terms: 0.4285714286 + 0.02040816328 = 0.44897959188
0.02040816328 + 0.2857142857x + x2 = 0.44897959188

Factor a perfect square on the left side:
(x + 0.1428571429)(x + 0.1428571429) = 0.44897959188

Calculate the square root of the right side: 0.670059394

Break this problem into two subproblems by setting 
(x + 0.1428571429) equal to 0.670059394 and -0.670059394.

Subproblem 1
x + 0.1428571429 = 0.670059394

Simplifying
x + 0.1428571429 = 0.670059394

Reorder the terms:
0.1428571429 + x = 0.670059394

Solving
0.1428571429 + x = 0.670059394

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = 0.670059394 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = 0.670059394 + -0.1428571429
x = 0.670059394 + -0.1428571429

Combine like terms: 0.670059394 + -0.1428571429 = 0.5272022511
x = 0.5272022511

Simplifying
x = 0.5272022511

Subproblem 2
x + 0.1428571429 = -0.670059394

Simplifying
x + 0.1428571429 = -0.670059394

Reorder the terms:
0.1428571429 + x = -0.670059394

Solving
0.1428571429 + x = -0.670059394

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = -0.670059394 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = -0.670059394 + -0.1428571429
x = -0.670059394 + -0.1428571429

Combine like terms: -0.670059394 + -0.1428571429 = -0.8129165369
x = -0.8129165369

Simplifying
x = -0.8129165369

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5272022511, -0.8129165369}