65x+5x(18-x)=10(-63)

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Solution for 65x+5x(18-x)=10(-63) equation: 


Simplifying
65x + 5x(18 + -1x) = 10(-63)
65x + (18 * 5x + -1x * 5x) = 10(-63)
65x + (90x + -5x2) = 10(-63)

Combine like terms: 65x + 90x = 155x
155x + -5x2 = 10(-63)

Multiply 10 * -63
155x + -5x2 = -630

Solving
155x + -5x2 = -630

Solving for variable 'x'.

Reorder the terms:
630 + 155x + -5x2 = -630 + 630

Combine like terms: -630 + 630 = 0
630 + 155x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(126 + 31x + -1x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(126 + 31x + -1x2)' equal to zero and attempt to solve:

Simplifying
126 + 31x + -1x2 = 0

Solving
126 + 31x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-126 + -31x + x2 = 0

Move the constant term to the right:

Add '126' to each side of the equation.
-126 + -31x + 126 + x2 = 0 + 126

Reorder the terms:
-126 + 126 + -31x + x2 = 0 + 126

Combine like terms: -126 + 126 = 0
0 + -31x + x2 = 0 + 126
-31x + x2 = 0 + 126

Combine like terms: 0 + 126 = 126
-31x + x2 = 126

The x term is -31x.  Take half its coefficient (-15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
-31x + 240.25 + x2 = 126 + 240.25

Reorder the terms:
240.25 + -31x + x2 = 126 + 240.25

Combine like terms: 126 + 240.25 = 366.25
240.25 + -31x + x2 = 366.25

Factor a perfect square on the left side:
(x + -15.5)(x + -15.5) = 366.25

Calculate the square root of the right side: 19.137659209

Break this problem into two subproblems by setting 
(x + -15.5) equal to 19.137659209 and -19.137659209.


Subproblem 1
x + -15.5 = 19.137659209

Simplifying
x + -15.5 = 19.137659209

Reorder the terms:
-15.5 + x = 19.137659209

Solving
-15.5 + x = 19.137659209

Solving for variable 'x'.

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

Add '15.5' to each side of the equation.
-15.5 + 15.5 + x = 19.137659209 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + x = 19.137659209 + 15.5
x = 19.137659209 + 15.5

Combine like terms: 19.137659209 + 15.5 = 34.637659209
x = 34.637659209

Simplifying
x = 34.637659209


Subproblem 2
x + -15.5 = -19.137659209

Simplifying
x + -15.5 = -19.137659209

Reorder the terms:
-15.5 + x = -19.137659209

Solving
-15.5 + x = -19.137659209

Solving for variable 'x'.

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

Add '15.5' to each side of the equation.
-15.5 + 15.5 + x = -19.137659209 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + x = -19.137659209 + 15.5
x = -19.137659209 + 15.5

Combine like terms: -19.137659209 + 15.5 = -3.637659209
x = -3.637659209

Simplifying
x = -3.637659209


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.637659209, -3.637659209}
Solution
x = {34.637659209, -3.637659209}

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