0=-2x^2-2x+4

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Solution for 0=-2x^2-2x+4 equation:


Simplifying
0 = -2x2 + -2x + 4

Reorder the terms:
0 = 4 + -2x + -2x2

Solving
0 = 4 + -2x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + 2x + 2x2 = 4 + -2x + -2x2 + -4 + 2x + 2x2

Reorder the terms:
-4 + 2x + 2x2 = 4 + -4 + -2x + 2x + -2x2 + 2x2

Combine like terms: 4 + -4 = 0
-4 + 2x + 2x2 = 0 + -2x + 2x + -2x2 + 2x2
-4 + 2x + 2x2 = -2x + 2x + -2x2 + 2x2

Combine like terms: -2x + 2x = 0
-4 + 2x + 2x2 = 0 + -2x2 + 2x2
-4 + 2x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-4 + 2x + 2x2 = 0

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

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

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

Solution

x = {-2, 1}

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