.05x+.12x(x+5000)=940

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Solution for .05x+.12x(x+5000)=940 equation:


Simplifying
0.05x + 0.12x(x + 5000) = 940

Reorder the terms:
0.05x + 0.12x(5000 + x) = 940
0.05x + (5000 * 0.12x + x * 0.12x) = 940
0.05x + (600x + 0.12x2) = 940

Combine like terms: 0.05x + 600x = 600.05x
600.05x + 0.12x2 = 940

Solving
600.05x + 0.12x2 = 940

Solving for variable 'x'.

Reorder the terms:
-940 + 600.05x + 0.12x2 = 940 + -940

Combine like terms: 940 + -940 = 0
-940 + 600.05x + 0.12x2 = 0

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

Divide each side by '0.12'.
-7833.333333 + 5000.416667x + x2 = 0

Move the constant term to the right:

Add '7833.333333' to each side of the equation.
-7833.333333 + 5000.416667x + 7833.333333 + x2 = 0 + 7833.333333

Reorder the terms:
-7833.333333 + 7833.333333 + 5000.416667x + x2 = 0 + 7833.333333

Combine like terms: -7833.333333 + 7833.333333 = 0.000000
0.000000 + 5000.416667x + x2 = 0 + 7833.333333
5000.416667x + x2 = 0 + 7833.333333

Combine like terms: 0 + 7833.333333 = 7833.333333
5000.416667x + x2 = 7833.333333

The x term is 5000.416667x.  Take half its coefficient (2500.208334).
Square it (6251041.713) and add it to both sides.

Add '6251041.713' to each side of the equation.
5000.416667x + 6251041.713 + x2 = 7833.333333 + 6251041.713

Reorder the terms:
6251041.713 + 5000.416667x + x2 = 7833.333333 + 6251041.713

Combine like terms: 7833.333333 + 6251041.713 = 6258875.046333
6251041.713 + 5000.416667x + x2 = 6258875.046333

Factor a perfect square on the left side:
(x + 2500.208334)(x + 2500.208334) = 6258875.046333

Calculate the square root of the right side: 2501.774379582

Break this problem into two subproblems by setting 
(x + 2500.208334) equal to 2501.774379582 and -2501.774379582.

Subproblem 1

x + 2500.208334 = 2501.774379582 Simplifying x + 2500.208334 = 2501.774379582 Reorder the terms: 2500.208334 + x = 2501.774379582 Solving 2500.208334 + x = 2501.774379582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2500.208334' to each side of the equation. 2500.208334 + -2500.208334 + x = 2501.774379582 + -2500.208334 Combine like terms: 2500.208334 + -2500.208334 = 0.000000 0.000000 + x = 2501.774379582 + -2500.208334 x = 2501.774379582 + -2500.208334 Combine like terms: 2501.774379582 + -2500.208334 = 1.566045582 x = 1.566045582 Simplifying x = 1.566045582

Subproblem 2

x + 2500.208334 = -2501.774379582 Simplifying x + 2500.208334 = -2501.774379582 Reorder the terms: 2500.208334 + x = -2501.774379582 Solving 2500.208334 + x = -2501.774379582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2500.208334' to each side of the equation. 2500.208334 + -2500.208334 + x = -2501.774379582 + -2500.208334 Combine like terms: 2500.208334 + -2500.208334 = 0.000000 0.000000 + x = -2501.774379582 + -2500.208334 x = -2501.774379582 + -2500.208334 Combine like terms: -2501.774379582 + -2500.208334 = -5001.982713582 x = -5001.982713582 Simplifying x = -5001.982713582

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.566045582, -5001.982713582}

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