x^2-29x-46=0

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Solution for x^2-29x-46=0 equation: 


Simplifying
x2 + -29x + -46 = 0

Reorder the terms:
-46 + -29x + x2 = 0

Solving
-46 + -29x + 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 + -29x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + -29x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -29x + x2 = 0 + 46
-29x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
-29x + x2 = 46

The x term is -29x.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x + 210.25 + x2 = 46 + 210.25

Reorder the terms:
210.25 + -29x + x2 = 46 + 210.25

Combine like terms: 46 + 210.25 = 256.25
210.25 + -29x + x2 = 256.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 256.25

Calculate the square root of the right side: 16.007810594

Break this problem into two subproblems by setting 
(x + -14.5) equal to 16.007810594 and -16.007810594.


Subproblem 1
x + -14.5 = 16.007810594

Simplifying
x + -14.5 = 16.007810594

Reorder the terms:
-14.5 + x = 16.007810594

Solving
-14.5 + x = 16.007810594

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = 16.007810594 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = 16.007810594 + 14.5
x = 16.007810594 + 14.5

Combine like terms: 16.007810594 + 14.5 = 30.507810594
x = 30.507810594

Simplifying
x = 30.507810594


Subproblem 2
x + -14.5 = -16.007810594

Simplifying
x + -14.5 = -16.007810594

Reorder the terms:
-14.5 + x = -16.007810594

Solving
-14.5 + x = -16.007810594

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = -16.007810594 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = -16.007810594 + 14.5
x = -16.007810594 + 14.5

Combine like terms: -16.007810594 + 14.5 = -1.507810594
x = -1.507810594

Simplifying
x = -1.507810594


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.507810594, -1.507810594}

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