x^2-14x+33=3

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Solution for x^2-14x+33=3 equation: 


Simplifying
x2 + -14x + 33 = 3

Reorder the terms:
33 + -14x + x2 = 3

Solving
33 + -14x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
33 + -3 + -14x + x2 = 3 + -3

Combine like terms: 33 + -3 = 30
30 + -14x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
30 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -14x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + -14x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -14x + x2 = 0 + -30
-14x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-14x + x2 = -30

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -30 + 49

Reorder the terms:
49 + -14x + x2 = -30 + 49

Combine like terms: -30 + 49 = 19
49 + -14x + x2 = 19

Factor a perfect square on the left side:
(x + -7)(x + -7) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -7) equal to 4.358898944 and -4.358898944.


Subproblem 1
x + -7 = 4.358898944

Simplifying
x + -7 = 4.358898944

Reorder the terms:
-7 + x = 4.358898944

Solving
-7 + x = 4.358898944

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 4.358898944 + 7

Combine like terms: -7 + 7 = 0
0 + x = 4.358898944 + 7
x = 4.358898944 + 7

Combine like terms: 4.358898944 + 7 = 11.358898944
x = 11.358898944

Simplifying
x = 11.358898944


Subproblem 2
x + -7 = -4.358898944

Simplifying
x + -7 = -4.358898944

Reorder the terms:
-7 + x = -4.358898944

Solving
-7 + x = -4.358898944

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -4.358898944 + 7

Combine like terms: -7 + 7 = 0
0 + x = -4.358898944 + 7
x = -4.358898944 + 7

Combine like terms: -4.358898944 + 7 = 2.641101056
x = 2.641101056

Simplifying
x = 2.641101056


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.358898944, 2.641101056}

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