(5x*5x+4x+2)-(5x*5)=7x+10

Solution for (5x*5x+4x+2)-(5x*5)=7x+10 equation:

Simplifying
(5x * 5x + 4x + 2) + -1(5x * 5) = 7x + 10

Reorder the terms for easier multiplication:
(5 * 5x * x + 4x + 2) + -1(5x * 5) = 7x + 10

Multiply 5 * 5
(25x * x + 4x + 2) + -1(5x * 5) = 7x + 10

Multiply x * x
(25x2 + 4x + 2) + -1(5x * 5) = 7x + 10

Reorder the terms:
(2 + 4x + 25x2) + -1(5x * 5) = 7x + 10

Remove parenthesis around (2 + 4x + 25x2)
2 + 4x + 25x2 + -1(5x * 5) = 7x + 10

Reorder the terms for easier multiplication:
2 + 4x + 25x2 + -1(5 * 5x) = 7x + 10

Multiply 5 * 5
2 + 4x + 25x2 + -1(25x) = 7x + 10

Remove parenthesis around (25x)
2 + 4x + 25x2 + -1 * 25x = 7x + 10

Multiply -1 * 25
2 + 4x + 25x2 + -25x = 7x + 10

Reorder the terms:
2 + 4x + -25x + 25x2 = 7x + 10

Combine like terms: 4x + -25x = -21x
2 + -21x + 25x2 = 7x + 10

Reorder the terms:
2 + -21x + 25x2 = 10 + 7x

Solving
2 + -21x + 25x2 = 10 + 7x

Solving for variable 'x'.

Reorder the terms:
2 + -10 + -21x + -7x + 25x2 = 10 + 7x + -10 + -7x

Combine like terms: 2 + -10 = -8
-8 + -21x + -7x + 25x2 = 10 + 7x + -10 + -7x

Combine like terms: -21x + -7x = -28x
-8 + -28x + 25x2 = 10 + 7x + -10 + -7x

Reorder the terms:
-8 + -28x + 25x2 = 10 + -10 + 7x + -7x

Combine like terms: 10 + -10 = 0
-8 + -28x + 25x2 = 0 + 7x + -7x
-8 + -28x + 25x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-8 + -28x + 25x2 = 0

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

Divide each side by '25'.
-0.32 + -1.12x + x2 = 0

Move the constant term to the right:

Add '0.32' to each side of the equation.
-0.32 + -1.12x + 0.32 + x2 = 0 + 0.32

Reorder the terms:
-0.32 + 0.32 + -1.12x + x2 = 0 + 0.32

Combine like terms: -0.32 + 0.32 = 0.00
0.00 + -1.12x + x2 = 0 + 0.32
-1.12x + x2 = 0 + 0.32

Combine like terms: 0 + 0.32 = 0.32
-1.12x + x2 = 0.32

The x term is -1.12x.  Take half its coefficient (-0.56).
Square it (0.3136) and add it to both sides.

Add '0.3136' to each side of the equation.
-1.12x + 0.3136 + x2 = 0.32 + 0.3136

Reorder the terms:
0.3136 + -1.12x + x2 = 0.32 + 0.3136

Combine like terms: 0.32 + 0.3136 = 0.6336
0.3136 + -1.12x + x2 = 0.6336

Factor a perfect square on the left side:
(x + -0.56)(x + -0.56) = 0.6336

Calculate the square root of the right side: 0.79598995

Break this problem into two subproblems by setting 
(x + -0.56) equal to 0.79598995 and -0.79598995.

Subproblem 1
x + -0.56 = 0.79598995

Simplifying
x + -0.56 = 0.79598995

Reorder the terms:
-0.56 + x = 0.79598995

Solving
-0.56 + x = 0.79598995

Solving for variable 'x'.

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

Add '0.56' to each side of the equation.
-0.56 + 0.56 + x = 0.79598995 + 0.56

Combine like terms: -0.56 + 0.56 = 0.00
0.00 + x = 0.79598995 + 0.56
x = 0.79598995 + 0.56

Combine like terms: 0.79598995 + 0.56 = 1.35598995
x = 1.35598995

Simplifying
x = 1.35598995

Subproblem 2
x + -0.56 = -0.79598995

Simplifying
x + -0.56 = -0.79598995

Reorder the terms:
-0.56 + x = -0.79598995

Solving
-0.56 + x = -0.79598995

Solving for variable 'x'.

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

Add '0.56' to each side of the equation.
-0.56 + 0.56 + x = -0.79598995 + 0.56

Combine like terms: -0.56 + 0.56 = 0.00
0.00 + x = -0.79598995 + 0.56
x = -0.79598995 + 0.56

Combine like terms: -0.79598995 + 0.56 = -0.23598995
x = -0.23598995

Simplifying
x = -0.23598995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.35598995, -0.23598995}