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

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


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

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

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

Add '5' to each side of the equation.
-5 + 5 + x = -5 + -2x + 5 + x2

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

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

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

Solving
x = -2x + x2

Solving for variable 'x'.

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

Reorder the terms:
3x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
3x + -1x2 = 0 + x2 + -1x2
3x + -1x2 = x2 + -1x2

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

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

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0, 3}

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