-2x^2-10x-3=0

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Solution for -2x^2-10x-3=0 equation: 


Simplifying
-2x2 + -10x + -3 = 0

Reorder the terms:
-3 + -10x + -2x2 = 0

Solving
-3 + -10x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 10x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 10x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + 10x + 2x2 = 0

Solving
3 + 10x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 5x + x2 = 0 + -1.5
5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
5x + x2 = -1.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -1.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -1.5 + 6.25

Combine like terms: -1.5 + 6.25 = 4.75
6.25 + 5x + x2 = 4.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.179449472 and -2.179449472.


Subproblem 1
x + 2.5 = 2.179449472

Simplifying
x + 2.5 = 2.179449472

Reorder the terms:
2.5 + x = 2.179449472

Solving
2.5 + x = 2.179449472

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.179449472 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.179449472 + -2.5
x = 2.179449472 + -2.5

Combine like terms: 2.179449472 + -2.5 = -0.320550528
x = -0.320550528

Simplifying
x = -0.320550528


Subproblem 2
x + 2.5 = -2.179449472

Simplifying
x + 2.5 = -2.179449472

Reorder the terms:
2.5 + x = -2.179449472

Solving
2.5 + x = -2.179449472

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.179449472 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.179449472 + -2.5
x = -2.179449472 + -2.5

Combine like terms: -2.179449472 + -2.5 = -4.679449472
x = -4.679449472

Simplifying
x = -4.679449472


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.320550528, -4.679449472}
Solution
x = {-0.320550528, -4.679449472}

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