x^2-14x-41=0

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Solution for x^2-14x-41=0 equation:


Simplifying
x2 + -14x + -41 = 0

Reorder the terms:
-41 + -14x + x2 = 0

Solving
-41 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + -14x + 41 + x2 = 0 + 41

Reorder the terms:
-41 + 41 + -14x + x2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -14x + x2 = 0 + 41
-14x + x2 = 0 + 41

Combine like terms: 0 + 41 = 41
-14x + x2 = 41

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 = 41 + 49

Reorder the terms:
49 + -14x + x2 = 41 + 49

Combine like terms: 41 + 49 = 90
49 + -14x + x2 = 90

Factor a perfect square on the left side:
(x + -7)(x + -7) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(x + -7) equal to 9.486832981 and -9.486832981.

Subproblem 1

x + -7 = 9.486832981 Simplifying x + -7 = 9.486832981 Reorder the terms: -7 + x = 9.486832981 Solving -7 + x = 9.486832981 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 = 9.486832981 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.486832981 + 7 x = 9.486832981 + 7 Combine like terms: 9.486832981 + 7 = 16.486832981 x = 16.486832981 Simplifying x = 16.486832981

Subproblem 2

x + -7 = -9.486832981 Simplifying x + -7 = -9.486832981 Reorder the terms: -7 + x = -9.486832981 Solving -7 + x = -9.486832981 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 = -9.486832981 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.486832981 + 7 x = -9.486832981 + 7 Combine like terms: -9.486832981 + 7 = -2.486832981 x = -2.486832981 Simplifying x = -2.486832981

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.486832981, -2.486832981}

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