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Simplifying 13p2 + -3p = 4209 Reorder the terms: -3p + 13p2 = 4209 Solving -3p + 13p2 = 4209 Solving for variable 'p'. Reorder the terms: -4209 + -3p + 13p2 = 4209 + -4209 Combine like terms: 4209 + -4209 = 0 -4209 + -3p + 13p2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -323.7692308 + -0.2307692308p + p2 = 0 Move the constant term to the right: Add '323.7692308' to each side of the equation. -323.7692308 + -0.2307692308p + 323.7692308 + p2 = 0 + 323.7692308 Reorder the terms: -323.7692308 + 323.7692308 + -0.2307692308p + p2 = 0 + 323.7692308 Combine like terms: -323.7692308 + 323.7692308 = 0.0000000 0.0000000 + -0.2307692308p + p2 = 0 + 323.7692308 -0.2307692308p + p2 = 0 + 323.7692308 Combine like terms: 0 + 323.7692308 = 323.7692308 -0.2307692308p + p2 = 323.7692308 The p term is -0.2307692308p. Take half its coefficient (-0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. -0.2307692308p + 0.01331360947 + p2 = 323.7692308 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308p + p2 = 323.7692308 + 0.01331360947 Combine like terms: 323.7692308 + 0.01331360947 = 323.78254440947 0.01331360947 + -0.2307692308p + p2 = 323.78254440947 Factor a perfect square on the left side: (p + -0.1153846154)(p + -0.1153846154) = 323.78254440947 Calculate the square root of the right side: 17.993958553 Break this problem into two subproblems by setting (p + -0.1153846154) equal to 17.993958553 and -17.993958553.Subproblem 1
p + -0.1153846154 = 17.993958553 Simplifying p + -0.1153846154 = 17.993958553 Reorder the terms: -0.1153846154 + p = 17.993958553 Solving -0.1153846154 + p = 17.993958553 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + p = 17.993958553 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + p = 17.993958553 + 0.1153846154 p = 17.993958553 + 0.1153846154 Combine like terms: 17.993958553 + 0.1153846154 = 18.1093431684 p = 18.1093431684 Simplifying p = 18.1093431684Subproblem 2
p + -0.1153846154 = -17.993958553 Simplifying p + -0.1153846154 = -17.993958553 Reorder the terms: -0.1153846154 + p = -17.993958553 Solving -0.1153846154 + p = -17.993958553 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + p = -17.993958553 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + p = -17.993958553 + 0.1153846154 p = -17.993958553 + 0.1153846154 Combine like terms: -17.993958553 + 0.1153846154 = -17.8785739376 p = -17.8785739376 Simplifying p = -17.8785739376Solution
The solution to the problem is based on the solutions from the subproblems. p = {18.1093431684, -17.8785739376}
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