32=x(2x+10)

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Solution for 32=x(2x+10) equation: 


Simplifying
32 = x(2x + 10)

Reorder the terms:
32 = x(10 + 2x)
32 = (10 * x + 2x * x)
32 = (10x + 2x2)

Solving
32 = 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
32 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
32 + -10x + -2x2 = 0 + 2x2 + -2x2
32 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
32 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -5x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
16 + -5x + -1x2 = 0

Solving
16 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-16 + 5x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 5x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 5x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 5x + x2 = 0 + 16
5x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
5x + x2 = 16

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 = 16 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 16 + 6.25

Combine like terms: 16 + 6.25 = 22.25
6.25 + 5x + x2 = 22.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
x + 2.5 = 4.716990566

Simplifying
x + 2.5 = 4.716990566

Reorder the terms:
2.5 + x = 4.716990566

Solving
2.5 + x = 4.716990566

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 = 4.716990566 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.716990566 + -2.5
x = 4.716990566 + -2.5

Combine like terms: 4.716990566 + -2.5 = 2.216990566
x = 2.216990566

Simplifying
x = 2.216990566


Subproblem 2
x + 2.5 = -4.716990566

Simplifying
x + 2.5 = -4.716990566

Reorder the terms:
2.5 + x = -4.716990566

Solving
2.5 + x = -4.716990566

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 = -4.716990566 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.716990566 + -2.5
x = -4.716990566 + -2.5

Combine like terms: -4.716990566 + -2.5 = -7.216990566
x = -7.216990566

Simplifying
x = -7.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.216990566, -7.216990566}
Solution
x = {2.216990566, -7.216990566}

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