4x^2-20x+17=1

Solution for 4x^2-20x+17=1 equation:

Simplifying
4x2 + -20x + 17 = 1

Reorder the terms:
17 + -20x + 4x2 = 1

Solving
17 + -20x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
17 + -1 + -20x + 4x2 = 1 + -1

Combine like terms: 17 + -1 = 16
16 + -20x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
16 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -5x + x2) = 0

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

Ignore the factor 4.
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 '(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 = {1, 4}