x^2-17x+49=3x

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Solution for x^2-17x+49=3x equation: 


Simplifying
x2 + -17x + 49 = 3x

Reorder the terms:
49 + -17x + x2 = 3x

Solving
49 + -17x + x2 = 3x

Solving for variable 'x'.

Reorder the terms:
49 + -17x + -3x + x2 = 3x + -3x

Combine like terms: -17x + -3x = -20x
49 + -20x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
49 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + -20x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + -20x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -20x + x2 = 0 + -49
-20x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
-20x + x2 = -49

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -49 + 100

Reorder the terms:
100 + -20x + x2 = -49 + 100

Combine like terms: -49 + 100 = 51
100 + -20x + x2 = 51

Factor a perfect square on the left side:
(x + -10)(x + -10) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + -10) equal to 7.141428429 and -7.141428429.


Subproblem 1
x + -10 = 7.141428429

Simplifying
x + -10 = 7.141428429

Reorder the terms:
-10 + x = 7.141428429

Solving
-10 + x = 7.141428429

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 7.141428429 + 10

Combine like terms: -10 + 10 = 0
0 + x = 7.141428429 + 10
x = 7.141428429 + 10

Combine like terms: 7.141428429 + 10 = 17.141428429
x = 17.141428429

Simplifying
x = 17.141428429


Subproblem 2
x + -10 = -7.141428429

Simplifying
x + -10 = -7.141428429

Reorder the terms:
-10 + x = -7.141428429

Solving
-10 + x = -7.141428429

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -7.141428429 + 10

Combine like terms: -10 + 10 = 0
0 + x = -7.141428429 + 10
x = -7.141428429 + 10

Combine like terms: -7.141428429 + 10 = 2.858571571
x = 2.858571571

Simplifying
x = 2.858571571


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.141428429, 2.858571571}

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