5x(5x+13)=7(7+24)

Solution for 5x(5x+13)=7(7+24) equation:

Simplifying
5x(5x + 13) = 7(7 + 24)

Reorder the terms:
5x(13 + 5x) = 7(7 + 24)
(13 * 5x + 5x * 5x) = 7(7 + 24)
(65x + 25x2) = 7(7 + 24)

Combine like terms: 7 + 24 = 31
65x + 25x2 = 7(31)

Multiply 7 * 31
65x + 25x2 = 217

Solving
65x + 25x2 = 217

Solving for variable 'x'.

Reorder the terms:
-217 + 65x + 25x2 = 217 + -217

Combine like terms: 217 + -217 = 0
-217 + 65x + 25x2 = 0

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

Divide each side by '25'.
-8.68 + 2.6x + x2 = 0

Move the constant term to the right:

Add '8.68' to each side of the equation.
-8.68 + 2.6x + 8.68 + x2 = 0 + 8.68

Reorder the terms:
-8.68 + 8.68 + 2.6x + x2 = 0 + 8.68

Combine like terms: -8.68 + 8.68 = 0.00
0.00 + 2.6x + x2 = 0 + 8.68
2.6x + x2 = 0 + 8.68

Combine like terms: 0 + 8.68 = 8.68
2.6x + x2 = 8.68

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 8.68 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 8.68 + 1.69

Combine like terms: 8.68 + 1.69 = 10.37
1.69 + 2.6x + x2 = 10.37

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 10.37

Calculate the square root of the right side: 3.220248438

Break this problem into two subproblems by setting 
(x + 1.3) equal to 3.220248438 and -3.220248438.

Subproblem 1
x + 1.3 = 3.220248438

Simplifying
x + 1.3 = 3.220248438

Reorder the terms:
1.3 + x = 3.220248438

Solving
1.3 + x = 3.220248438

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = 3.220248438 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = 3.220248438 + -1.3
x = 3.220248438 + -1.3

Combine like terms: 3.220248438 + -1.3 = 1.920248438
x = 1.920248438

Simplifying
x = 1.920248438

Subproblem 2
x + 1.3 = -3.220248438

Simplifying
x + 1.3 = -3.220248438

Reorder the terms:
1.3 + x = -3.220248438

Solving
1.3 + x = -3.220248438

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = -3.220248438 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = -3.220248438 + -1.3
x = -3.220248438 + -1.3

Combine like terms: -3.220248438 + -1.3 = -4.520248438
x = -4.520248438

Simplifying
x = -4.520248438

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.920248438, -4.520248438}