x^2-20x-46=0

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Solution for x^2-20x-46=0 equation: 


Simplifying
x2 + -20x + -46 = 0

Reorder the terms:
-46 + -20x + x2 = 0

Solving
-46 + -20x + 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 + -20x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + -20x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -20x + x2 = 0 + 46
-20x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
-20x + x2 = 46

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 46 + 100

Reorder the terms:
100 + -20x + x2 = 46 + 100

Combine like terms: 46 + 100 = 146
100 + -20x + x2 = 146

Factor a perfect square on the left side:
(x + -10)(x + -10) = 146

Calculate the square root of the right side: 12.083045974

Break this problem into two subproblems by setting 
(x + -10) equal to 12.083045974 and -12.083045974.


Subproblem 1
x + -10 = 12.083045974

Simplifying
x + -10 = 12.083045974

Reorder the terms:
-10 + x = 12.083045974

Solving
-10 + x = 12.083045974

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 12.083045974 + 10

Combine like terms: -10 + 10 = 0
0 + x = 12.083045974 + 10
x = 12.083045974 + 10

Combine like terms: 12.083045974 + 10 = 22.083045974
x = 22.083045974

Simplifying
x = 22.083045974


Subproblem 2
x + -10 = -12.083045974

Simplifying
x + -10 = -12.083045974

Reorder the terms:
-10 + x = -12.083045974

Solving
-10 + x = -12.083045974

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -12.083045974 + 10

Combine like terms: -10 + 10 = 0
0 + x = -12.083045974 + 10
x = -12.083045974 + 10

Combine like terms: -12.083045974 + 10 = -2.083045974
x = -2.083045974

Simplifying
x = -2.083045974


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.083045974, -2.083045974}

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