25+3x(x-8)=106

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Solution for 25+3x(x-8)=106 equation: 


Simplifying
25 + 3x(x + -8) = 106

Reorder the terms:
25 + 3x(-8 + x) = 106
25 + (-8 * 3x + x * 3x) = 106
25 + (-24x + 3x2) = 106

Solving
25 + -24x + 3x2 = 106

Solving for variable 'x'.

Reorder the terms:
25 + -106 + -24x + 3x2 = 106 + -106

Combine like terms: 25 + -106 = -81
-81 + -24x + 3x2 = 106 + -106

Combine like terms: 106 + -106 = 0
-81 + -24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-27 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-27 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-27 + -8x + x2 = 0

Solving
-27 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -8x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -8x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -8x + x2 = 0 + 27
-8x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-8x + x2 = 27

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 = 27 + 16

Reorder the terms:
16 + -8x + x2 = 27 + 16

Combine like terms: 27 + 16 = 43
16 + -8x + x2 = 43

Factor a perfect square on the left side:
(x + -4)(x + -4) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(x + -4) equal to 6.557438524 and -6.557438524.


Subproblem 1
x + -4 = 6.557438524

Simplifying
x + -4 = 6.557438524

Reorder the terms:
-4 + x = 6.557438524

Solving
-4 + x = 6.557438524

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 = 6.557438524 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6.557438524 + 4
x = 6.557438524 + 4

Combine like terms: 6.557438524 + 4 = 10.557438524
x = 10.557438524

Simplifying
x = 10.557438524


Subproblem 2
x + -4 = -6.557438524

Simplifying
x + -4 = -6.557438524

Reorder the terms:
-4 + x = -6.557438524

Solving
-4 + x = -6.557438524

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 = -6.557438524 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6.557438524 + 4
x = -6.557438524 + 4

Combine like terms: -6.557438524 + 4 = -2.557438524
x = -2.557438524

Simplifying
x = -2.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.557438524, -2.557438524}
Solution
x = {10.557438524, -2.557438524}

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