2x^2-2x+1=25

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Solution for 2x^2-2x+1=25 equation:


Simplifying
2x2 + -2x + 1 = 25

Reorder the terms:
1 + -2x + 2x2 = 25

Solving
1 + -2x + 2x2 = 25

Solving for variable 'x'.

Reorder the terms:
1 + -25 + -2x + 2x2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + -2x + 2x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-3, 4}

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