5x^2-30x-50=0

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Solution for 5x^2-30x-50=0 equation: 


Simplifying
5x2 + -30x + -50 = 0

Reorder the terms:
-50 + -30x + 5x2 = 0

Solving
-50 + -30x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + -6x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-10 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-10 + -6x + x2 = 0

Solving
-10 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -6x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -6x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -6x + x2 = 0 + 10
-6x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-6x + x2 = 10

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 10 + 9

Reorder the terms:
9 + -6x + x2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + -6x + x2 = 19

Factor a perfect square on the left side:
(x + -3)(x + -3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -3) equal to 4.358898944 and -4.358898944.


Subproblem 1
x + -3 = 4.358898944

Simplifying
x + -3 = 4.358898944

Reorder the terms:
-3 + x = 4.358898944

Solving
-3 + x = 4.358898944

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.358898944 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.358898944 + 3
x = 4.358898944 + 3

Combine like terms: 4.358898944 + 3 = 7.358898944
x = 7.358898944

Simplifying
x = 7.358898944


Subproblem 2
x + -3 = -4.358898944

Simplifying
x + -3 = -4.358898944

Reorder the terms:
-3 + x = -4.358898944

Solving
-3 + x = -4.358898944

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.358898944 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.358898944 + 3
x = -4.358898944 + 3

Combine like terms: -4.358898944 + 3 = -1.358898944
x = -1.358898944

Simplifying
x = -1.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.358898944, -1.358898944}
Solution
x = {7.358898944, -1.358898944}

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