0.07p+0.09p(7000-p)=530

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Solution for 0.07p+0.09p(7000-p)=530 equation:


Simplifying
0.07p + 0.09p(7000 + -1p) = 530
0.07p + (7000 * 0.09p + -1p * 0.09p) = 530
0.07p + (630p + -0.09p2) = 530

Combine like terms: 0.07p + 630p = 630.07p
630.07p + -0.09p2 = 530

Solving
630.07p + -0.09p2 = 530

Solving for variable 'p'.

Reorder the terms:
-530 + 630.07p + -0.09p2 = 530 + -530

Combine like terms: 530 + -530 = 0
-530 + 630.07p + -0.09p2 = 0

Begin completing the square.  Divide all terms by
-0.09 the coefficient of the squared term: 

Divide each side by '-0.09'.
5888.888889 + -7000.777778p + p2 = 0

Move the constant term to the right:

Add '-5888.888889' to each side of the equation.
5888.888889 + -7000.777778p + -5888.888889 + p2 = 0 + -5888.888889

Reorder the terms:
5888.888889 + -5888.888889 + -7000.777778p + p2 = 0 + -5888.888889

Combine like terms: 5888.888889 + -5888.888889 = 0.000000
0.000000 + -7000.777778p + p2 = 0 + -5888.888889
-7000.777778p + p2 = 0 + -5888.888889

Combine like terms: 0 + -5888.888889 = -5888.888889
-7000.777778p + p2 = -5888.888889

The p term is -7000.777778p.  Take half its coefficient (-3500.388889).
Square it (12252722.37) and add it to both sides.

Add '12252722.37' to each side of the equation.
-7000.777778p + 12252722.37 + p2 = -5888.888889 + 12252722.37

Reorder the terms:
12252722.37 + -7000.777778p + p2 = -5888.888889 + 12252722.37

Combine like terms: -5888.888889 + 12252722.37 = 12246833.481111
12252722.37 + -7000.777778p + p2 = 12246833.481111

Factor a perfect square on the left side:
(p + -3500.388889)(p + -3500.388889) = 12246833.481111

Calculate the square root of the right side: 3499.547610922

Break this problem into two subproblems by setting 
(p + -3500.388889) equal to 3499.547610922 and -3499.547610922.

Subproblem 1

p + -3500.388889 = 3499.547610922 Simplifying p + -3500.388889 = 3499.547610922 Reorder the terms: -3500.388889 + p = 3499.547610922 Solving -3500.388889 + p = 3499.547610922 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3500.388889' to each side of the equation. -3500.388889 + 3500.388889 + p = 3499.547610922 + 3500.388889 Combine like terms: -3500.388889 + 3500.388889 = 0.000000 0.000000 + p = 3499.547610922 + 3500.388889 p = 3499.547610922 + 3500.388889 Combine like terms: 3499.547610922 + 3500.388889 = 6999.936499922 p = 6999.936499922 Simplifying p = 6999.936499922

Subproblem 2

p + -3500.388889 = -3499.547610922 Simplifying p + -3500.388889 = -3499.547610922 Reorder the terms: -3500.388889 + p = -3499.547610922 Solving -3500.388889 + p = -3499.547610922 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3500.388889' to each side of the equation. -3500.388889 + 3500.388889 + p = -3499.547610922 + 3500.388889 Combine like terms: -3500.388889 + 3500.388889 = 0.000000 0.000000 + p = -3499.547610922 + 3500.388889 p = -3499.547610922 + 3500.388889 Combine like terms: -3499.547610922 + 3500.388889 = 0.841278078 p = 0.841278078 Simplifying p = 0.841278078

Solution

The solution to the problem is based on the solutions from the subproblems. p = {6999.936499922, 0.841278078}

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