-5x^2-125x-45=0

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Solution for -5x^2-125x-45=0 equation:


Simplifying
-5x2 + -125x + -45 = 0

Reorder the terms:
-45 + -125x + -5x2 = 0

Solving
-45 + -125x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-5'.
-5(9 + 25x + x2) = 0

Ignore the factor -5.

Subproblem 1
Set the factor '(9 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
9 + 25x + x2 = 0

Solving
9 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 25x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 25x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 25x + x2 = 0 + -9
25x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
25x + x2 = -9

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = -9 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -9 + 156.25

Combine like terms: -9 + 156.25 = 147.25
156.25 + 25x + x2 = 147.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 147.25

Calculate the square root of the right side: 12.1346611

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.1346611 and -12.1346611.


Subproblem 1
x + 12.5 = 12.1346611

Simplifying
x + 12.5 = 12.1346611

Reorder the terms:
12.5 + x = 12.1346611

Solving
12.5 + x = 12.1346611

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 12.1346611 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 12.1346611 + -12.5
x = 12.1346611 + -12.5

Combine like terms: 12.1346611 + -12.5 = -0.3653389
x = -0.3653389

Simplifying
x = -0.3653389


Subproblem 2
x + 12.5 = -12.1346611

Simplifying
x + 12.5 = -12.1346611

Reorder the terms:
12.5 + x = -12.1346611

Solving
12.5 + x = -12.1346611

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -12.1346611 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -12.1346611 + -12.5
x = -12.1346611 + -12.5

Combine like terms: -12.1346611 + -12.5 = -24.6346611
x = -24.6346611

Simplifying
x = -24.6346611


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.3653389, -24.6346611}
Solution
x = {-0.3653389, -24.6346611}

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