1750=(x+5)(x)(3.5)

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Solution for 1750=(x+5)(x)(3.5) equation: 


Simplifying
1750 = (x + 5)(x)(3.5)

Reorder the terms:
1750 = (5 + x)(x)(3.5)

Reorder the terms for easier multiplication:
1750 = 3.5x(5 + x)
1750 = (5 * 3.5x + x * 3.5x)
1750 = (17.5x + 3.5x2)

Solving
1750 = 17.5x + 3.5x2

Solving for variable 'x'.

Reorder the terms:
1750 + -17.5x + -3.5x2 = 17.5x + -17.5x + 3.5x2 + -3.5x2

Combine like terms: 17.5x + -17.5x = 0.0
1750 + -17.5x + -3.5x2 = 0.0 + 3.5x2 + -3.5x2
1750 + -17.5x + -3.5x2 = 3.5x2 + -3.5x2

Combine like terms: 3.5x2 + -3.5x2 = 0.0
1750 + -17.5x + -3.5x2 = 0.0

Begin completing the square.  Divide all terms by
-3.5 the coefficient of the squared term: 

Divide each side by '-3.5'.
-500 + 5x + x2 = 0

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 5x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + 5x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 5x + x2 = 0 + 500
5x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
5x + x2 = 500

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 500 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 500 + 6.25

Combine like terms: 500 + 6.25 = 506.25
6.25 + 5x + x2 = 506.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 506.25

Calculate the square root of the right side: 22.5

Break this problem into two subproblems by setting 
(x + 2.5) equal to 22.5 and -22.5.


Subproblem 1
x + 2.5 = 22.5

Simplifying
x + 2.5 = 22.5

Reorder the terms:
2.5 + x = 22.5

Solving
2.5 + x = 22.5

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 22.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 22.5 + -2.5
x = 22.5 + -2.5

Combine like terms: 22.5 + -2.5 = 20
x = 20

Simplifying
x = 20


Subproblem 2
x + 2.5 = -22.5

Simplifying
x + 2.5 = -22.5

Reorder the terms:
2.5 + x = -22.5

Solving
2.5 + x = -22.5

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -22.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -22.5 + -2.5
x = -22.5 + -2.5

Combine like terms: -22.5 + -2.5 = -25
x = -25

Simplifying
x = -25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20, -25}

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