40(x)(5x+14)=80

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Solution for 40(x)(5x+14)=80 equation: 


Simplifying
40(x)(5x + 14) = 80

Reorder the terms:
40x(14 + 5x) = 80
(14 * 40x + 5x * 40x) = 80
(560x + 200x2) = 80

Solving
560x + 200x2 = 80

Solving for variable 'x'.

Reorder the terms:
-80 + 560x + 200x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 560x + 200x2 = 0

Factor out the Greatest Common Factor (GCF), '40'.
40(-2 + 14x + 5x2) = 0

Ignore the factor 40.

Subproblem 1
Set the factor '(-2 + 14x + 5x2)' equal to zero and attempt to solve:

Simplifying
-2 + 14x + 5x2 = 0

Solving
-2 + 14x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + 2.8x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 2.8x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 2.8x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 2.8x + x2 = 0 + 0.4
2.8x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
2.8x + x2 = 0.4

The x term is 2.8x.  Take half its coefficient (1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
2.8x + 1.96 + x2 = 0.4 + 1.96

Reorder the terms:
1.96 + 2.8x + x2 = 0.4 + 1.96

Combine like terms: 0.4 + 1.96 = 2.36
1.96 + 2.8x + x2 = 2.36

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = 2.36

Calculate the square root of the right side: 1.53622915

Break this problem into two subproblems by setting 
(x + 1.4) equal to 1.53622915 and -1.53622915.


Subproblem 1
x + 1.4 = 1.53622915

Simplifying
x + 1.4 = 1.53622915

Reorder the terms:
1.4 + x = 1.53622915

Solving
1.4 + x = 1.53622915

Solving for variable 'x'.

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

Add '-1.4' to each side of the equation.
1.4 + -1.4 + x = 1.53622915 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = 1.53622915 + -1.4
x = 1.53622915 + -1.4

Combine like terms: 1.53622915 + -1.4 = 0.13622915
x = 0.13622915

Simplifying
x = 0.13622915


Subproblem 2
x + 1.4 = -1.53622915

Simplifying
x + 1.4 = -1.53622915

Reorder the terms:
1.4 + x = -1.53622915

Solving
1.4 + x = -1.53622915

Solving for variable 'x'.

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

Add '-1.4' to each side of the equation.
1.4 + -1.4 + x = -1.53622915 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = -1.53622915 + -1.4
x = -1.53622915 + -1.4

Combine like terms: -1.53622915 + -1.4 = -2.93622915
x = -2.93622915

Simplifying
x = -2.93622915


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.13622915, -2.93622915}
Solution
x = {0.13622915, -2.93622915}

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