x(4x+10)+20=180

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Solution for x(4x+10)+20=180 equation: 


Simplifying
x(4x + 10) + 20 = 180

Reorder the terms:
x(10 + 4x) + 20 = 180
(10 * x + 4x * x) + 20 = 180
(10x + 4x2) + 20 = 180

Reorder the terms:
20 + 10x + 4x2 = 180

Solving
20 + 10x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
20 + -180 + 10x + 4x2 = 180 + -180

Combine like terms: 20 + -180 = -160
-160 + 10x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-160 + 10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-80 + 5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-80 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-80 + 5x + 2x2 = 0

Solving
-80 + 5x + 2x2 = 0

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

Divide each side by '2'.
-40 + 2.5x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 2.5x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 2.5x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 2.5x + x2 = 0 + 40
2.5x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
2.5x + x2 = 40

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 40 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 40 + 1.5625

Combine like terms: 40 + 1.5625 = 41.5625
1.5625 + 2.5x + x2 = 41.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 41.5625

Calculate the square root of the right side: 6.446898479

Break this problem into two subproblems by setting 
(x + 1.25) equal to 6.446898479 and -6.446898479.


Subproblem 1
x + 1.25 = 6.446898479

Simplifying
x + 1.25 = 6.446898479

Reorder the terms:
1.25 + x = 6.446898479

Solving
1.25 + x = 6.446898479

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 6.446898479 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 6.446898479 + -1.25
x = 6.446898479 + -1.25

Combine like terms: 6.446898479 + -1.25 = 5.196898479
x = 5.196898479

Simplifying
x = 5.196898479


Subproblem 2
x + 1.25 = -6.446898479

Simplifying
x + 1.25 = -6.446898479

Reorder the terms:
1.25 + x = -6.446898479

Solving
1.25 + x = -6.446898479

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -6.446898479 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -6.446898479 + -1.25
x = -6.446898479 + -1.25

Combine like terms: -6.446898479 + -1.25 = -7.696898479
x = -7.696898479

Simplifying
x = -7.696898479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.196898479, -7.696898479}
Solution
x = {5.196898479, -7.696898479}

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