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Simplifying 9p + 16 = p2 Reorder the terms: 16 + 9p = p2 Solving 16 + 9p = p2 Solving for variable 'p'. Combine like terms: p2 + -1p2 = 0 16 + 9p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + -9p + p2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -9p + 16 + p2 = 0 + 16 Reorder the terms: -16 + 16 + -9p + p2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -9p + p2 = 0 + 16 -9p + p2 = 0 + 16 Combine like terms: 0 + 16 = 16 -9p + p2 = 16 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = 16 + 20.25 Reorder the terms: 20.25 + -9p + p2 = 16 + 20.25 Combine like terms: 16 + 20.25 = 36.25 20.25 + -9p + p2 = 36.25 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (p + -4.5) equal to 6.020797289 and -6.020797289.Subproblem 1
p + -4.5 = 6.020797289 Simplifying p + -4.5 = 6.020797289 Reorder the terms: -4.5 + p = 6.020797289 Solving -4.5 + p = 6.020797289 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 6.020797289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 6.020797289 + 4.5 p = 6.020797289 + 4.5 Combine like terms: 6.020797289 + 4.5 = 10.520797289 p = 10.520797289 Simplifying p = 10.520797289Subproblem 2
p + -4.5 = -6.020797289 Simplifying p + -4.5 = -6.020797289 Reorder the terms: -4.5 + p = -6.020797289 Solving -4.5 + p = -6.020797289 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -6.020797289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -6.020797289 + 4.5 p = -6.020797289 + 4.5 Combine like terms: -6.020797289 + 4.5 = -1.520797289 p = -1.520797289 Simplifying p = -1.520797289Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.520797289, -1.520797289}
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