5x*5x-15x-50=0

Solution for 5x*5x-15x-50=0 equation:

Simplifying
5x * 5x + -15x + -50 = 0

Reorder the terms for easier multiplication:
5 * 5x * x + -15x + -50 = 0

Multiply 5 * 5
25x * x + -15x + -50 = 0

Multiply x * x
25x2 + -15x + -50 = 0

Reorder the terms:
-50 + -15x + 25x2 = 0

Solving
-50 + -15x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + -3x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-10 + -3x + 5x2)' equal to zero and attempt to solve:

Simplifying
-10 + -3x + 5x2 = 0

Solving
-10 + -3x + 5x2 = 0

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

Divide each side by '5'.
-2 + -0.6x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.6x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.6x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.6x + x2 = 0 + 2
-0.6x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.6x + x2 = 2

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 2 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 2 + 0.09

Combine like terms: 2 + 0.09 = 2.09
0.09 + -0.6x + x2 = 2.09

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 2.09

Calculate the square root of the right side: 1.445683229

Break this problem into two subproblems by setting 
(x + -0.3) equal to 1.445683229 and -1.445683229.

Subproblem 1
x + -0.3 = 1.445683229

Simplifying
x + -0.3 = 1.445683229

Reorder the terms:
-0.3 + x = 1.445683229

Solving
-0.3 + x = 1.445683229

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 1.445683229 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 1.445683229 + 0.3
x = 1.445683229 + 0.3

Combine like terms: 1.445683229 + 0.3 = 1.745683229
x = 1.745683229

Simplifying
x = 1.745683229

Subproblem 2
x + -0.3 = -1.445683229

Simplifying
x + -0.3 = -1.445683229

Reorder the terms:
-0.3 + x = -1.445683229

Solving
-0.3 + x = -1.445683229

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -1.445683229 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -1.445683229 + 0.3
x = -1.445683229 + 0.3

Combine like terms: -1.445683229 + 0.3 = -1.145683229
x = -1.145683229

Simplifying
x = -1.145683229

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.745683229, -1.145683229}
Solution
x = {1.745683229, -1.145683229}