2x(x+40)=680

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Solution for 2x(x+40)=680 equation: 


Simplifying
2x(x + 40) = 680

Reorder the terms:
2x(40 + x) = 680
(40 * 2x + x * 2x) = 680
(80x + 2x2) = 680

Solving
80x + 2x2 = 680

Solving for variable 'x'.

Reorder the terms:
-680 + 80x + 2x2 = 680 + -680

Combine like terms: 680 + -680 = 0
-680 + 80x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-340 + 40x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-340 + 40x + x2)' equal to zero and attempt to solve:

Simplifying
-340 + 40x + x2 = 0

Solving
-340 + 40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '340' to each side of the equation.
-340 + 40x + 340 + x2 = 0 + 340

Reorder the terms:
-340 + 340 + 40x + x2 = 0 + 340

Combine like terms: -340 + 340 = 0
0 + 40x + x2 = 0 + 340
40x + x2 = 0 + 340

Combine like terms: 0 + 340 = 340
40x + x2 = 340

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = 340 + 400

Reorder the terms:
400 + 40x + x2 = 340 + 400

Combine like terms: 340 + 400 = 740
400 + 40x + x2 = 740

Factor a perfect square on the left side:
(x + 20)(x + 20) = 740

Calculate the square root of the right side: 27.202941017

Break this problem into two subproblems by setting 
(x + 20) equal to 27.202941017 and -27.202941017.


Subproblem 1
x + 20 = 27.202941017

Simplifying
x + 20 = 27.202941017

Reorder the terms:
20 + x = 27.202941017

Solving
20 + x = 27.202941017

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = 27.202941017 + -20

Combine like terms: 20 + -20 = 0
0 + x = 27.202941017 + -20
x = 27.202941017 + -20

Combine like terms: 27.202941017 + -20 = 7.202941017
x = 7.202941017

Simplifying
x = 7.202941017


Subproblem 2
x + 20 = -27.202941017

Simplifying
x + 20 = -27.202941017

Reorder the terms:
20 + x = -27.202941017

Solving
20 + x = -27.202941017

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = -27.202941017 + -20

Combine like terms: 20 + -20 = 0
0 + x = -27.202941017 + -20
x = -27.202941017 + -20

Combine like terms: -27.202941017 + -20 = -47.202941017
x = -47.202941017

Simplifying
x = -47.202941017


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.202941017, -47.202941017}
Solution
x = {7.202941017, -47.202941017}

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