x^2-8x-29=0

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Solution for x^2-8x-29=0 equation:


Simplifying
x2 + -8x + -29 = 0

Reorder the terms:
-29 + -8x + x2 = 0

Solving
-29 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -8x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + -8x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -8x + x2 = 0 + 29
-8x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
-8x + x2 = 29

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 29 + 16

Reorder the terms:
16 + -8x + x2 = 29 + 16

Combine like terms: 29 + 16 = 45
16 + -8x + x2 = 45

Factor a perfect square on the left side:
(x + -4)(x + -4) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -4) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + -4 = 6.708203933

Simplifying
x + -4 = 6.708203933

Reorder the terms:
-4 + x = 6.708203933

Solving
-4 + x = 6.708203933

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 6.708203933 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6.708203933 + 4
x = 6.708203933 + 4

Combine like terms: 6.708203933 + 4 = 10.708203933
x = 10.708203933

Simplifying
x = 10.708203933


Subproblem 2
x + -4 = -6.708203933

Simplifying
x + -4 = -6.708203933

Reorder the terms:
-4 + x = -6.708203933

Solving
-4 + x = -6.708203933

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -6.708203933 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6.708203933 + 4
x = -6.708203933 + 4

Combine like terms: -6.708203933 + 4 = -2.708203933
x = -2.708203933

Simplifying
x = -2.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.708203933, -2.708203933}

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