.70x+.25(100)=.60x(x+100)

Solution for .70x+.25(100)=.60x(x+100) equation:

Simplifying
0.70x + 0.25(100) = 0.60x(x + 100)

Multiply 0.25 * 100
0.70x + 25 = 0.60x(x + 100)

Reorder the terms:
25 + 0.70x = 0.60x(x + 100)

Reorder the terms:
25 + 0.70x = 0.60x(100 + x)
25 + 0.70x = (100 * 0.60x + x * 0.60x)
25 + 0.70x = (60x + 0.60x2)

Solving
25 + 0.70x = 60x + 0.60x2

Solving for variable 'x'.

Combine like terms: 0.70x + -60x = -59.3x
25 + -59.3x + -0.60x2 = 60x + 0.60x2 + -60x + -0.60x2

Reorder the terms:
25 + -59.3x + -0.60x2 = 60x + -60x + 0.60x2 + -0.60x2

Combine like terms: 60x + -60x = 0
25 + -59.3x + -0.60x2 = 0 + 0.60x2 + -0.60x2
25 + -59.3x + -0.60x2 = 0.60x2 + -0.60x2

Combine like terms: 0.60x2 + -0.60x2 = 0.00
25 + -59.3x + -0.60x2 = 0.00

Begin completing the square.  Divide all terms by
-0.60 the coefficient of the squared term: 

Divide each side by '-0.60'.
-41.66666667 + 98.83333333x + x2 = 0

Move the constant term to the right:

Add '41.66666667' to each side of the equation.
-41.66666667 + 98.83333333x + 41.66666667 + x2 = 0 + 41.66666667

Reorder the terms:
-41.66666667 + 41.66666667 + 98.83333333x + x2 = 0 + 41.66666667

Combine like terms: -41.66666667 + 41.66666667 = 0.00000000
0.00000000 + 98.83333333x + x2 = 0 + 41.66666667
98.83333333x + x2 = 0 + 41.66666667

Combine like terms: 0 + 41.66666667 = 41.66666667
98.83333333x + x2 = 41.66666667

The x term is 98.83333333x.  Take half its coefficient (49.41666667).
Square it (2442.006945) and add it to both sides.

Add '2442.006945' to each side of the equation.
98.83333333x + 2442.006945 + x2 = 41.66666667 + 2442.006945

Reorder the terms:
2442.006945 + 98.83333333x + x2 = 41.66666667 + 2442.006945

Combine like terms: 41.66666667 + 2442.006945 = 2483.67361167
2442.006945 + 98.83333333x + x2 = 2483.67361167

Factor a perfect square on the left side:
(x + 49.41666667)(x + 49.41666667) = 2483.67361167

Calculate the square root of the right side: 49.836468692

Break this problem into two subproblems by setting 
(x + 49.41666667) equal to 49.836468692 and -49.836468692.

Subproblem 1
x + 49.41666667 = 49.836468692

Simplifying
x + 49.41666667 = 49.836468692

Reorder the terms:
49.41666667 + x = 49.836468692

Solving
49.41666667 + x = 49.836468692

Solving for variable 'x'.

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

Add '-49.41666667' to each side of the equation.
49.41666667 + -49.41666667 + x = 49.836468692 + -49.41666667

Combine like terms: 49.41666667 + -49.41666667 = 0.00000000
0.00000000 + x = 49.836468692 + -49.41666667
x = 49.836468692 + -49.41666667

Combine like terms: 49.836468692 + -49.41666667 = 0.419802022
x = 0.419802022

Simplifying
x = 0.419802022

Subproblem 2
x + 49.41666667 = -49.836468692

Simplifying
x + 49.41666667 = -49.836468692

Reorder the terms:
49.41666667 + x = -49.836468692

Solving
49.41666667 + x = -49.836468692

Solving for variable 'x'.

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

Add '-49.41666667' to each side of the equation.
49.41666667 + -49.41666667 + x = -49.836468692 + -49.41666667

Combine like terms: 49.41666667 + -49.41666667 = 0.00000000
0.00000000 + x = -49.836468692 + -49.41666667
x = -49.836468692 + -49.41666667

Combine like terms: -49.836468692 + -49.41666667 = -99.253135362
x = -99.253135362

Simplifying
x = -99.253135362

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.419802022, -99.253135362}