.15x+.07x(70000-x)=5000

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Solution for .15x+.07x(70000-x)=5000 equation:


Simplifying
0.15x + 0.07x(70000 + -1x) = 5000
0.15x + (70000 * 0.07x + -1x * 0.07x) = 5000
0.15x + (4900x + -0.07x2) = 5000

Combine like terms: 0.15x + 4900x = 4900.15x
4900.15x + -0.07x2 = 5000

Solving
4900.15x + -0.07x2 = 5000

Solving for variable 'x'.

Reorder the terms:
-5000 + 4900.15x + -0.07x2 = 5000 + -5000

Combine like terms: 5000 + -5000 = 0
-5000 + 4900.15x + -0.07x2 = 0

Begin completing the square.  Divide all terms by
-0.07 the coefficient of the squared term: 

Divide each side by '-0.07'.
71428.57143 + -70002.14286x + x2 = 0

Move the constant term to the right:

Add '-71428.57143' to each side of the equation.
71428.57143 + -70002.14286x + -71428.57143 + x2 = 0 + -71428.57143

Reorder the terms:
71428.57143 + -71428.57143 + -70002.14286x + x2 = 0 + -71428.57143

Combine like terms: 71428.57143 + -71428.57143 = 0.00000
0.00000 + -70002.14286x + x2 = 0 + -71428.57143
-70002.14286x + x2 = 0 + -71428.57143

Combine like terms: 0 + -71428.57143 = -71428.57143
-70002.14286x + x2 = -71428.57143

The x term is -70002.14286x.  Take half its coefficient (-35001.07143).
Square it (1225075001) and add it to both sides.

Add '1225075001' to each side of the equation.
-70002.14286x + 1225075001 + x2 = -71428.57143 + 1225075001

Reorder the terms:
1225075001 + -70002.14286x + x2 = -71428.57143 + 1225075001

Combine like terms: -71428.57143 + 1225075001 = 1225003572.42857
1225075001 + -70002.14286x + x2 = 1225003572.42857

Factor a perfect square on the left side:
(x + -35001.07143)(x + -35001.07143) = 1225003572.42857

Calculate the square root of the right side: 35000.051034657

Break this problem into two subproblems by setting 
(x + -35001.07143) equal to 35000.051034657 and -35000.051034657.

Subproblem 1

x + -35001.07143 = 35000.051034657 Simplifying x + -35001.07143 = 35000.051034657 Reorder the terms: -35001.07143 + x = 35000.051034657 Solving -35001.07143 + x = 35000.051034657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35001.07143' to each side of the equation. -35001.07143 + 35001.07143 + x = 35000.051034657 + 35001.07143 Combine like terms: -35001.07143 + 35001.07143 = 0.00000 0.00000 + x = 35000.051034657 + 35001.07143 x = 35000.051034657 + 35001.07143 Combine like terms: 35000.051034657 + 35001.07143 = 70001.122464657 x = 70001.122464657 Simplifying x = 70001.122464657

Subproblem 2

x + -35001.07143 = -35000.051034657 Simplifying x + -35001.07143 = -35000.051034657 Reorder the terms: -35001.07143 + x = -35000.051034657 Solving -35001.07143 + x = -35000.051034657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35001.07143' to each side of the equation. -35001.07143 + 35001.07143 + x = -35000.051034657 + 35001.07143 Combine like terms: -35001.07143 + 35001.07143 = 0.00000 0.00000 + x = -35000.051034657 + 35001.07143 x = -35000.051034657 + 35001.07143 Combine like terms: -35000.051034657 + 35001.07143 = 1.020395343 x = 1.020395343 Simplifying x = 1.020395343

Solution

The solution to the problem is based on the solutions from the subproblems. x = {70001.122464657, 1.020395343}

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