0.07x+0.04x(110000-x)=660

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Solution for 0.07x+0.04x(110000-x)=660 equation:


Simplifying
0.07x + 0.04x(110000 + -1x) = 660
0.07x + (110000 * 0.04x + -1x * 0.04x) = 660
0.07x + (4400x + -0.04x2) = 660

Combine like terms: 0.07x + 4400x = 4400.07x
4400.07x + -0.04x2 = 660

Solving
4400.07x + -0.04x2 = 660

Solving for variable 'x'.

Reorder the terms:
-660 + 4400.07x + -0.04x2 = 660 + -660

Combine like terms: 660 + -660 = 0
-660 + 4400.07x + -0.04x2 = 0

Begin completing the square.  Divide all terms by
-0.04 the coefficient of the squared term: 

Divide each side by '-0.04'.
16500 + -110001.75x + x2 = 0

Move the constant term to the right:

Add '-16500' to each side of the equation.
16500 + -110001.75x + -16500 + x2 = 0 + -16500

Reorder the terms:
16500 + -16500 + -110001.75x + x2 = 0 + -16500

Combine like terms: 16500 + -16500 = 0
0 + -110001.75x + x2 = 0 + -16500
-110001.75x + x2 = 0 + -16500

Combine like terms: 0 + -16500 = -16500
-110001.75x + x2 = -16500

The x term is -110001.75x.  Take half its coefficient (-55000.875).
Square it (3025096251) and add it to both sides.

Add '3025096251' to each side of the equation.
-110001.75x + 3025096251 + x2 = -16500 + 3025096251

Reorder the terms:
3025096251 + -110001.75x + x2 = -16500 + 3025096251

Combine like terms: -16500 + 3025096251 = 3025079751
3025096251 + -110001.75x + x2 = 3025079751

Factor a perfect square on the left side:
(x + -55000.875)(x + -55000.875) = 3025079751

Calculate the square root of the right side: 55000.725004312

Break this problem into two subproblems by setting 
(x + -55000.875) equal to 55000.725004312 and -55000.725004312.

Subproblem 1

x + -55000.875 = 55000.725004312 Simplifying x + -55000.875 = 55000.725004312 Reorder the terms: -55000.875 + x = 55000.725004312 Solving -55000.875 + x = 55000.725004312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55000.875' to each side of the equation. -55000.875 + 55000.875 + x = 55000.725004312 + 55000.875 Combine like terms: -55000.875 + 55000.875 = 0.000 0.000 + x = 55000.725004312 + 55000.875 x = 55000.725004312 + 55000.875 Combine like terms: 55000.725004312 + 55000.875 = 110001.600004312 x = 110001.600004312 Simplifying x = 110001.600004312

Subproblem 2

x + -55000.875 = -55000.725004312 Simplifying x + -55000.875 = -55000.725004312 Reorder the terms: -55000.875 + x = -55000.725004312 Solving -55000.875 + x = -55000.725004312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55000.875' to each side of the equation. -55000.875 + 55000.875 + x = -55000.725004312 + 55000.875 Combine like terms: -55000.875 + 55000.875 = 0.000 0.000 + x = -55000.725004312 + 55000.875 x = -55000.725004312 + 55000.875 Combine like terms: -55000.725004312 + 55000.875 = 0.149995688 x = 0.149995688 Simplifying x = 0.149995688

Solution

The solution to the problem is based on the solutions from the subproblems. x = {110001.600004312, 0.149995688}

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