2x(2x+1)=2

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Solution for 2x(2x+1)=2 equation:


Simplifying
2x(2x + 1) = 2

Reorder the terms:
2x(1 + 2x) = 2
(1 * 2x + 2x * 2x) = 2
(2x + 4x2) = 2

Solving
2x + 4x2 = 2

Solving for variable 'x'.

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

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

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

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-1, 0.5}

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