x^2-19x-46=0

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Solution for x^2-19x-46=0 equation: 


Simplifying
x2 + -19x + -46 = 0

Reorder the terms:
-46 + -19x + x2 = 0

Solving
-46 + -19x + 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 + -19x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + -19x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -19x + x2 = 0 + 46
-19x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
-19x + x2 = 46

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = 46 + 90.25

Reorder the terms:
90.25 + -19x + x2 = 46 + 90.25

Combine like terms: 46 + 90.25 = 136.25
90.25 + -19x + x2 = 136.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 136.25

Calculate the square root of the right side: 11.67261753

Break this problem into two subproblems by setting 
(x + -9.5) equal to 11.67261753 and -11.67261753.


Subproblem 1
x + -9.5 = 11.67261753

Simplifying
x + -9.5 = 11.67261753

Reorder the terms:
-9.5 + x = 11.67261753

Solving
-9.5 + x = 11.67261753

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 11.67261753 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 11.67261753 + 9.5
x = 11.67261753 + 9.5

Combine like terms: 11.67261753 + 9.5 = 21.17261753
x = 21.17261753

Simplifying
x = 21.17261753


Subproblem 2
x + -9.5 = -11.67261753

Simplifying
x + -9.5 = -11.67261753

Reorder the terms:
-9.5 + x = -11.67261753

Solving
-9.5 + x = -11.67261753

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -11.67261753 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -11.67261753 + 9.5
x = -11.67261753 + 9.5

Combine like terms: -11.67261753 + 9.5 = -2.17261753
x = -2.17261753

Simplifying
x = -2.17261753


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.17261753, -2.17261753}

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