2x+5=x^2-x-5

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


Simplifying
2x + 5 = x2 + -1x + -5

Reorder the terms:
5 + 2x = x2 + -1x + -5

Reorder the terms:
5 + 2x = -5 + -1x + x2

Solving
5 + 2x = -5 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
5 + 5 + 2x + x + -1x2 = -5 + -1x + x2 + 5 + x + -1x2

Combine like terms: 5 + 5 = 10
10 + 2x + x + -1x2 = -5 + -1x + x2 + 5 + x + -1x2

Combine like terms: 2x + x = 3x
10 + 3x + -1x2 = -5 + -1x + x2 + 5 + x + -1x2

Reorder the terms:
10 + 3x + -1x2 = -5 + 5 + -1x + x + x2 + -1x2

Combine like terms: -5 + 5 = 0
10 + 3x + -1x2 = 0 + -1x + x + x2 + -1x2
10 + 3x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
10 + 3x + -1x2 = 0 + x2 + -1x2
10 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 3x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(2 + x) = 0


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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {5, -2}

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