2x(x)+5x(25-x)=7(x+24)

Solution for 2x(x)+5x(25-x)=7(x+24) equation:

Simplifying
2x(x) + 5x(25 + -1x) = 7(x + 24)

Multiply x * x
2x2 + 5x(25 + -1x) = 7(x + 24)
2x2 + (25 * 5x + -1x * 5x) = 7(x + 24)
2x2 + (125x + -5x2) = 7(x + 24)

Reorder the terms:
125x + 2x2 + -5x2 = 7(x + 24)

Combine like terms: 2x2 + -5x2 = -3x2
125x + -3x2 = 7(x + 24)

Reorder the terms:
125x + -3x2 = 7(24 + x)
125x + -3x2 = (24 * 7 + x * 7)
125x + -3x2 = (168 + 7x)

Solving
125x + -3x2 = 168 + 7x

Solving for variable 'x'.

Reorder the terms:
-168 + 125x + -7x + -3x2 = 168 + 7x + -168 + -7x

Combine like terms: 125x + -7x = 118x
-168 + 118x + -3x2 = 168 + 7x + -168 + -7x

Reorder the terms:
-168 + 118x + -3x2 = 168 + -168 + 7x + -7x

Combine like terms: 168 + -168 = 0
-168 + 118x + -3x2 = 0 + 7x + -7x
-168 + 118x + -3x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-168 + 118x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
56 + -39.33333333x + x2 = 0

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + -39.33333333x + -56 + x2 = 0 + -56

Reorder the terms:
56 + -56 + -39.33333333x + x2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -39.33333333x + x2 = 0 + -56
-39.33333333x + x2 = 0 + -56

Combine like terms: 0 + -56 = -56
-39.33333333x + x2 = -56

The x term is -39.33333333x.  Take half its coefficient (-19.66666667).
Square it (386.7777779) and add it to both sides.

Add '386.7777779' to each side of the equation.
-39.33333333x + 386.7777779 + x2 = -56 + 386.7777779

Reorder the terms:
386.7777779 + -39.33333333x + x2 = -56 + 386.7777779

Combine like terms: -56 + 386.7777779 = 330.7777779
386.7777779 + -39.33333333x + x2 = 330.7777779

Factor a perfect square on the left side:
(x + -19.66666667)(x + -19.66666667) = 330.7777779

Calculate the square root of the right side: 18.187297158

Break this problem into two subproblems by setting 
(x + -19.66666667) equal to 18.187297158 and -18.187297158.

Subproblem 1
x + -19.66666667 = 18.187297158

Simplifying
x + -19.66666667 = 18.187297158

Reorder the terms:
-19.66666667 + x = 18.187297158

Solving
-19.66666667 + x = 18.187297158

Solving for variable 'x'.

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

Add '19.66666667' to each side of the equation.
-19.66666667 + 19.66666667 + x = 18.187297158 + 19.66666667

Combine like terms: -19.66666667 + 19.66666667 = 0.00000000
0.00000000 + x = 18.187297158 + 19.66666667
x = 18.187297158 + 19.66666667

Combine like terms: 18.187297158 + 19.66666667 = 37.853963828
x = 37.853963828

Simplifying
x = 37.853963828

Subproblem 2
x + -19.66666667 = -18.187297158

Simplifying
x + -19.66666667 = -18.187297158

Reorder the terms:
-19.66666667 + x = -18.187297158

Solving
-19.66666667 + x = -18.187297158

Solving for variable 'x'.

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

Add '19.66666667' to each side of the equation.
-19.66666667 + 19.66666667 + x = -18.187297158 + 19.66666667

Combine like terms: -19.66666667 + 19.66666667 = 0.00000000
0.00000000 + x = -18.187297158 + 19.66666667
x = -18.187297158 + 19.66666667

Combine like terms: -18.187297158 + 19.66666667 = 1.479369512
x = 1.479369512

Simplifying
x = 1.479369512

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.853963828, 1.479369512}