a^2=2a-1

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Solution for a^2=2a-1 equation:


Simplifying
a2 = 2a + -1

Reorder the terms:
a2 = -1 + 2a

Solving
a2 = -1 + 2a

Solving for variable 'a'.

Reorder the terms:
1 + -2a + a2 = -1 + 2a + 1 + -2a

Reorder the terms:
1 + -2a + a2 = -1 + 1 + 2a + -2a

Combine like terms: -1 + 1 = 0
1 + -2a + a2 = 0 + 2a + -2a
1 + -2a + a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
1 + -2a + a2 = 0

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

Subproblem 1

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

Subproblem 2

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

Solution

a = {1, 1}

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