x=-2x^2-5x-10

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Solution for x=-2x^2-5x-10 equation:


Simplifying
x = -2x2 + -5x + -10

Reorder the terms:
x = -10 + -5x + -2x2

Solving
x = -10 + -5x + -2x2

Solving for variable 'x'.

Reorder the terms:
10 + x + 5x + 2x2 = -10 + -5x + -2x2 + 10 + 5x + 2x2

Combine like terms: x + 5x = 6x
10 + 6x + 2x2 = -10 + -5x + -2x2 + 10 + 5x + 2x2

Reorder the terms:
10 + 6x + 2x2 = -10 + 10 + -5x + 5x + -2x2 + 2x2

Combine like terms: -10 + 10 = 0
10 + 6x + 2x2 = 0 + -5x + 5x + -2x2 + 2x2
10 + 6x + 2x2 = -5x + 5x + -2x2 + 2x2

Combine like terms: -5x + 5x = 0
10 + 6x + 2x2 = 0 + -2x2 + 2x2
10 + 6x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
10 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 3x + x2) = 0

Ignore the factor 2.

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

Simplifying
5 + 3x + x2 = 0

Solving
5 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 3x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 3x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x + x2 = 0 + -5
3x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
3x + x2 = -5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -5 + 2.25

Combine like terms: -5 + 2.25 = -2.75
2.25 + 3x + x2 = -2.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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