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Simplifying 4p2 + 15p + -19 = 9 Reorder the terms: -19 + 15p + 4p2 = 9 Solving -19 + 15p + 4p2 = 9 Solving for variable 'p'. Reorder the terms: -19 + -9 + 15p + 4p2 = 9 + -9 Combine like terms: -19 + -9 = -28 -28 + 15p + 4p2 = 9 + -9 Combine like terms: 9 + -9 = 0 -28 + 15p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7 + 3.75p + p2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 3.75p + 7 + p2 = 0 + 7 Reorder the terms: -7 + 7 + 3.75p + p2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3.75p + p2 = 0 + 7 3.75p + p2 = 0 + 7 Combine like terms: 0 + 7 = 7 3.75p + p2 = 7 The p term is 3.75p. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75p + 3.515625 + p2 = 7 + 3.515625 Reorder the terms: 3.515625 + 3.75p + p2 = 7 + 3.515625 Combine like terms: 7 + 3.515625 = 10.515625 3.515625 + 3.75p + p2 = 10.515625 Factor a perfect square on the left side: (p + 1.875)(p + 1.875) = 10.515625 Calculate the square root of the right side: 3.242780443 Break this problem into two subproblems by setting (p + 1.875) equal to 3.242780443 and -3.242780443.Subproblem 1
p + 1.875 = 3.242780443 Simplifying p + 1.875 = 3.242780443 Reorder the terms: 1.875 + p = 3.242780443 Solving 1.875 + p = 3.242780443 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + p = 3.242780443 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + p = 3.242780443 + -1.875 p = 3.242780443 + -1.875 Combine like terms: 3.242780443 + -1.875 = 1.367780443 p = 1.367780443 Simplifying p = 1.367780443Subproblem 2
p + 1.875 = -3.242780443 Simplifying p + 1.875 = -3.242780443 Reorder the terms: 1.875 + p = -3.242780443 Solving 1.875 + p = -3.242780443 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + p = -3.242780443 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + p = -3.242780443 + -1.875 p = -3.242780443 + -1.875 Combine like terms: -3.242780443 + -1.875 = -5.117780443 p = -5.117780443 Simplifying p = -5.117780443Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.367780443, -5.117780443}
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