X^2-16X+64=2X+19

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Solution for X^2-16X+64=2X+19 equation: 


Simplifying
X2 + -16X + 64 = 2X + 19

Reorder the terms:
64 + -16X + X2 = 2X + 19

Reorder the terms:
64 + -16X + X2 = 19 + 2X

Solving
64 + -16X + X2 = 19 + 2X

Solving for variable 'X'.

Reorder the terms:
64 + -19 + -16X + -2X + X2 = 19 + 2X + -19 + -2X

Combine like terms: 64 + -19 = 45
45 + -16X + -2X + X2 = 19 + 2X + -19 + -2X

Combine like terms: -16X + -2X = -18X
45 + -18X + X2 = 19 + 2X + -19 + -2X

Reorder the terms:
45 + -18X + X2 = 19 + -19 + 2X + -2X

Combine like terms: 19 + -19 = 0
45 + -18X + X2 = 0 + 2X + -2X
45 + -18X + X2 = 2X + -2X

Combine like terms: 2X + -2X = 0
45 + -18X + X2 = 0

Factor a trinomial.
(3 + -1X)(15 + -1X) = 0


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 '(15 + -1X)' equal to zero and attempt to solve:

Simplifying
15 + -1X = 0

Solving
15 + -1X = 0

Move all terms containing X to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + -1X = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1X = 0 + -15
-1X = 0 + -15

Combine like terms: 0 + -15 = -15
-1X = -15

Divide each side by '-1'.
X = 15

Simplifying
X = 15
Solution
X = {3, 15}

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