x^2-14x+46=0

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Solution for x^2-14x+46=0 equation: 


Simplifying
x2 + -14x + 46 = 0

Reorder the terms:
46 + -14x + x2 = 0

Solving
46 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + -14x + -46 + x2 = 0 + -46

Reorder the terms:
46 + -46 + -14x + x2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -14x + x2 = 0 + -46
-14x + x2 = 0 + -46

Combine like terms: 0 + -46 = -46
-14x + x2 = -46

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 = -46 + 49

Reorder the terms:
49 + -14x + x2 = -46 + 49

Combine like terms: -46 + 49 = 3
49 + -14x + x2 = 3

Factor a perfect square on the left side:
(x + -7)(x + -7) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -7) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -7 = 1.732050808

Simplifying
x + -7 = 1.732050808

Reorder the terms:
-7 + x = 1.732050808

Solving
-7 + x = 1.732050808

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 = 1.732050808 + 7

Combine like terms: -7 + 7 = 0
0 + x = 1.732050808 + 7
x = 1.732050808 + 7

Combine like terms: 1.732050808 + 7 = 8.732050808
x = 8.732050808

Simplifying
x = 8.732050808


Subproblem 2
x + -7 = -1.732050808

Simplifying
x + -7 = -1.732050808

Reorder the terms:
-7 + x = -1.732050808

Solving
-7 + x = -1.732050808

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 = -1.732050808 + 7

Combine like terms: -7 + 7 = 0
0 + x = -1.732050808 + 7
x = -1.732050808 + 7

Combine like terms: -1.732050808 + 7 = 5.267949192
x = 5.267949192

Simplifying
x = 5.267949192


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.732050808, 5.267949192}

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