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Simplifying -5p2 + 650p + 3000 = 0 Reorder the terms: 3000 + 650p + -5p2 = 0 Solving 3000 + 650p + -5p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(600 + 130p + -1p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(600 + 130p + -1p2)' equal to zero and attempt to solve: Simplifying 600 + 130p + -1p2 = 0 Solving 600 + 130p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -600 + -130p + p2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + -130p + 600 + p2 = 0 + 600 Reorder the terms: -600 + 600 + -130p + p2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -130p + p2 = 0 + 600 -130p + p2 = 0 + 600 Combine like terms: 0 + 600 = 600 -130p + p2 = 600 The p term is -130p. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130p + 4225 + p2 = 600 + 4225 Reorder the terms: 4225 + -130p + p2 = 600 + 4225 Combine like terms: 600 + 4225 = 4825 4225 + -130p + p2 = 4825 Factor a perfect square on the left side: (p + -65)(p + -65) = 4825 Calculate the square root of the right side: 69.462219947 Break this problem into two subproblems by setting (p + -65) equal to 69.462219947 and -69.462219947.Subproblem 1
p + -65 = 69.462219947 Simplifying p + -65 = 69.462219947 Reorder the terms: -65 + p = 69.462219947 Solving -65 + p = 69.462219947 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + p = 69.462219947 + 65 Combine like terms: -65 + 65 = 0 0 + p = 69.462219947 + 65 p = 69.462219947 + 65 Combine like terms: 69.462219947 + 65 = 134.462219947 p = 134.462219947 Simplifying p = 134.462219947Subproblem 2
p + -65 = -69.462219947 Simplifying p + -65 = -69.462219947 Reorder the terms: -65 + p = -69.462219947 Solving -65 + p = -69.462219947 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + p = -69.462219947 + 65 Combine like terms: -65 + 65 = 0 0 + p = -69.462219947 + 65 p = -69.462219947 + 65 Combine like terms: -69.462219947 + 65 = -4.462219947 p = -4.462219947 Simplifying p = -4.462219947Solution
The solution to the problem is based on the solutions from the subproblems. p = {134.462219947, -4.462219947}Solution
p = {134.462219947, -4.462219947}
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