4x^2+40x=180

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Solution for 4x^2+40x=180 equation: 


Simplifying
4x2 + 40x = 180

Reorder the terms:
40x + 4x2 = 180

Solving
40x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 40x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 10x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 10x + x2 = 0

Solving
-45 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 10x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 10x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 10x + x2 = 0 + 45
10x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
10x + x2 = 45

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 45 + 25

Reorder the terms:
25 + 10x + x2 = 45 + 25

Combine like terms: 45 + 25 = 70
25 + 10x + x2 = 70

Factor a perfect square on the left side:
(x + 5)(x + 5) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + 5) equal to 8.366600265 and -8.366600265.


Subproblem 1
x + 5 = 8.366600265

Simplifying
x + 5 = 8.366600265

Reorder the terms:
5 + x = 8.366600265

Solving
5 + x = 8.366600265

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 8.366600265 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.366600265 + -5
x = 8.366600265 + -5

Combine like terms: 8.366600265 + -5 = 3.366600265
x = 3.366600265

Simplifying
x = 3.366600265


Subproblem 2
x + 5 = -8.366600265

Simplifying
x + 5 = -8.366600265

Reorder the terms:
5 + x = -8.366600265

Solving
5 + x = -8.366600265

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -8.366600265 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.366600265 + -5
x = -8.366600265 + -5

Combine like terms: -8.366600265 + -5 = -13.366600265
x = -13.366600265

Simplifying
x = -13.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.366600265, -13.366600265}
Solution
x = {3.366600265, -13.366600265}

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