2x(35+100x)=1000

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Solution for 2x(35+100x)=1000 equation: 


Simplifying
2x(35 + 100x) = 1000
(35 * 2x + 100x * 2x) = 1000
(70x + 200x2) = 1000

Solving
70x + 200x2 = 1000

Solving for variable 'x'.

Reorder the terms:
-1000 + 70x + 200x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-1000 + 70x + 200x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-100 + 7x + 20x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-100 + 7x + 20x2)' equal to zero and attempt to solve:

Simplifying
-100 + 7x + 20x2 = 0

Solving
-100 + 7x + 20x2 = 0

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

Divide each side by '20'.
-5 + 0.35x + x2 = 0.0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 0.35x + 5 + x2 = 0.0 + 5

Reorder the terms:
-5 + 5 + 0.35x + x2 = 0.0 + 5

Combine like terms: -5 + 5 = 0
0 + 0.35x + x2 = 0.0 + 5
0.35x + x2 = 0.0 + 5

Combine like terms: 0.0 + 5 = 5
0.35x + x2 = 5

The x term is 0.35x.  Take half its coefficient (0.175).
Square it (0.030625) and add it to both sides.

Add '0.030625' to each side of the equation.
0.35x + 0.030625 + x2 = 5 + 0.030625

Reorder the terms:
0.030625 + 0.35x + x2 = 5 + 0.030625

Combine like terms: 5 + 0.030625 = 5.030625
0.030625 + 0.35x + x2 = 5.030625

Factor a perfect square on the left side:
(x + 0.175)(x + 0.175) = 5.030625

Calculate the square root of the right side: 2.242905482

Break this problem into two subproblems by setting 
(x + 0.175) equal to 2.242905482 and -2.242905482.


Subproblem 1
x + 0.175 = 2.242905482

Simplifying
x + 0.175 = 2.242905482

Reorder the terms:
0.175 + x = 2.242905482

Solving
0.175 + x = 2.242905482

Solving for variable 'x'.

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

Add '-0.175' to each side of the equation.
0.175 + -0.175 + x = 2.242905482 + -0.175

Combine like terms: 0.175 + -0.175 = 0.000
0.000 + x = 2.242905482 + -0.175
x = 2.242905482 + -0.175

Combine like terms: 2.242905482 + -0.175 = 2.067905482
x = 2.067905482

Simplifying
x = 2.067905482


Subproblem 2
x + 0.175 = -2.242905482

Simplifying
x + 0.175 = -2.242905482

Reorder the terms:
0.175 + x = -2.242905482

Solving
0.175 + x = -2.242905482

Solving for variable 'x'.

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

Add '-0.175' to each side of the equation.
0.175 + -0.175 + x = -2.242905482 + -0.175

Combine like terms: 0.175 + -0.175 = 0.000
0.000 + x = -2.242905482 + -0.175
x = -2.242905482 + -0.175

Combine like terms: -2.242905482 + -0.175 = -2.417905482
x = -2.417905482

Simplifying
x = -2.417905482


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.067905482, -2.417905482}
Solution
x = {2.067905482, -2.417905482}

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