x^2-14x+41=-3

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Solution for x^2-14x+41=-3 equation: 


Simplifying
x2 + -14x + 41 = -3

Reorder the terms:
41 + -14x + x2 = -3

Solving
41 + -14x + x2 = -3

Solving for variable 'x'.

Reorder the terms:
41 + 3 + -14x + x2 = -3 + 3

Combine like terms: 41 + 3 = 44
44 + -14x + x2 = -3 + 3

Combine like terms: -3 + 3 = 0
44 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + -14x + -44 + x2 = 0 + -44

Reorder the terms:
44 + -44 + -14x + x2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + -14x + x2 = 0 + -44
-14x + x2 = 0 + -44

Combine like terms: 0 + -44 = -44
-14x + x2 = -44

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 = -44 + 49

Reorder the terms:
49 + -14x + x2 = -44 + 49

Combine like terms: -44 + 49 = 5
49 + -14x + x2 = 5

Factor a perfect square on the left side:
(x + -7)(x + -7) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -7) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -7 = 2.236067978

Simplifying
x + -7 = 2.236067978

Reorder the terms:
-7 + x = 2.236067978

Solving
-7 + x = 2.236067978

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 = 2.236067978 + 7

Combine like terms: -7 + 7 = 0
0 + x = 2.236067978 + 7
x = 2.236067978 + 7

Combine like terms: 2.236067978 + 7 = 9.236067978
x = 9.236067978

Simplifying
x = 9.236067978


Subproblem 2
x + -7 = -2.236067978

Simplifying
x + -7 = -2.236067978

Reorder the terms:
-7 + x = -2.236067978

Solving
-7 + x = -2.236067978

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 = -2.236067978 + 7

Combine like terms: -7 + 7 = 0
0 + x = -2.236067978 + 7
x = -2.236067978 + 7

Combine like terms: -2.236067978 + 7 = 4.763932022
x = 4.763932022

Simplifying
x = 4.763932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.236067978, 4.763932022}

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