220=(2x+7)(x)

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Solution for 220=(2x+7)(x) equation: 


Simplifying
220 = (2x + 7)(x)

Reorder the terms:
220 = (7 + 2x)(x)

Reorder the terms for easier multiplication:
220 = x(7 + 2x)
220 = (7 * x + 2x * x)
220 = (7x + 2x2)

Solving
220 = 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
220 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
220 + -7x + -2x2 = 0 + 2x2 + -2x2
220 + -7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
220 + -7x + -2x2 = 0

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

Divide each side by '-2'.
-110 + 3.5x + x2 = 0

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + 3.5x + 110 + x2 = 0 + 110

Reorder the terms:
-110 + 110 + 3.5x + x2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + 3.5x + x2 = 0 + 110
3.5x + x2 = 0 + 110

Combine like terms: 0 + 110 = 110
3.5x + x2 = 110

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 110 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 110 + 3.0625

Combine like terms: 110 + 3.0625 = 113.0625
3.0625 + 3.5x + x2 = 113.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 113.0625

Calculate the square root of the right side: 10.633085159

Break this problem into two subproblems by setting 
(x + 1.75) equal to 10.633085159 and -10.633085159.


Subproblem 1
x + 1.75 = 10.633085159

Simplifying
x + 1.75 = 10.633085159

Reorder the terms:
1.75 + x = 10.633085159

Solving
1.75 + x = 10.633085159

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 10.633085159 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 10.633085159 + -1.75
x = 10.633085159 + -1.75

Combine like terms: 10.633085159 + -1.75 = 8.883085159
x = 8.883085159

Simplifying
x = 8.883085159


Subproblem 2
x + 1.75 = -10.633085159

Simplifying
x + 1.75 = -10.633085159

Reorder the terms:
1.75 + x = -10.633085159

Solving
1.75 + x = -10.633085159

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -10.633085159 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -10.633085159 + -1.75
x = -10.633085159 + -1.75

Combine like terms: -10.633085159 + -1.75 = -12.383085159
x = -12.383085159

Simplifying
x = -12.383085159


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.883085159, -12.383085159}

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