420=(2x+5)(x)

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Solution for 420=(2x+5)(x) equation: 


Simplifying
420 = (2x + 5)(x)

Reorder the terms:
420 = (5 + 2x)(x)

Reorder the terms for easier multiplication:
420 = x(5 + 2x)
420 = (5 * x + 2x * x)
420 = (5x + 2x2)

Solving
420 = 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
420 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
420 + -5x + -2x2 = 0 + 2x2 + -2x2
420 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
420 + -5x + -2x2 = 0

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

Divide each side by '-2'.
-210 + 2.5x + x2 = 0

Move the constant term to the right:

Add '210' to each side of the equation.
-210 + 2.5x + 210 + x2 = 0 + 210

Reorder the terms:
-210 + 210 + 2.5x + x2 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + 2.5x + x2 = 0 + 210
2.5x + x2 = 0 + 210

Combine like terms: 0 + 210 = 210
2.5x + x2 = 210

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 = 210 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 210 + 1.5625

Combine like terms: 210 + 1.5625 = 211.5625
1.5625 + 2.5x + x2 = 211.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 211.5625

Calculate the square root of the right side: 14.545188208

Break this problem into two subproblems by setting 
(x + 1.25) equal to 14.545188208 and -14.545188208.


Subproblem 1
x + 1.25 = 14.545188208

Simplifying
x + 1.25 = 14.545188208

Reorder the terms:
1.25 + x = 14.545188208

Solving
1.25 + x = 14.545188208

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 = 14.545188208 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 14.545188208 + -1.25
x = 14.545188208 + -1.25

Combine like terms: 14.545188208 + -1.25 = 13.295188208
x = 13.295188208

Simplifying
x = 13.295188208


Subproblem 2
x + 1.25 = -14.545188208

Simplifying
x + 1.25 = -14.545188208

Reorder the terms:
1.25 + x = -14.545188208

Solving
1.25 + x = -14.545188208

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 = -14.545188208 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -14.545188208 + -1.25
x = -14.545188208 + -1.25

Combine like terms: -14.545188208 + -1.25 = -15.795188208
x = -15.795188208

Simplifying
x = -15.795188208


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.295188208, -15.795188208}

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