x^2-3x+8x-32=0

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Solution for x^2-3x+8x-32=0 equation: 


Simplifying
x2 + -3x + 8x + -32 = 0

Reorder the terms:
-32 + -3x + 8x + x2 = 0

Combine like terms: -3x + 8x = 5x
-32 + 5x + x2 = 0

Solving
-32 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 5x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 5x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 5x + x2 = 0 + 32
5x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
5x + x2 = 32

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 32 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 32 + 6.25

Combine like terms: 32 + 6.25 = 38.25
6.25 + 5x + x2 = 38.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
x + 2.5 = 6.184658438

Simplifying
x + 2.5 = 6.184658438

Reorder the terms:
2.5 + x = 6.184658438

Solving
2.5 + x = 6.184658438

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 6.184658438 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 6.184658438 + -2.5
x = 6.184658438 + -2.5

Combine like terms: 6.184658438 + -2.5 = 3.684658438
x = 3.684658438

Simplifying
x = 3.684658438


Subproblem 2
x + 2.5 = -6.184658438

Simplifying
x + 2.5 = -6.184658438

Reorder the terms:
2.5 + x = -6.184658438

Solving
2.5 + x = -6.184658438

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -6.184658438 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -6.184658438 + -2.5
x = -6.184658438 + -2.5

Combine like terms: -6.184658438 + -2.5 = -8.684658438
x = -8.684658438

Simplifying
x = -8.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.684658438, -8.684658438}

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