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Simplifying p * p + -2p = 9 Multiply p * p p2 + -2p = 9 Reorder the terms: -2p + p2 = 9 Solving -2p + p2 = 9 Solving for variable 'p'. Reorder the terms: -9 + -2p + p2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -2p + 9 + p2 = 0 + 9 Reorder the terms: -9 + 9 + -2p + p2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2p + p2 = 0 + 9 -2p + p2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2p + p2 = 9 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 9 + 1 Reorder the terms: 1 + -2p + p2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + -2p + p2 = 10 Factor a perfect square on the left side: (p + -1)(p + -1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (p + -1) equal to 3.16227766 and -3.16227766.Subproblem 1
p + -1 = 3.16227766 Simplifying p + -1 = 3.16227766 Reorder the terms: -1 + p = 3.16227766 Solving -1 + p = 3.16227766 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + p = 3.16227766 + 1 p = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 p = 4.16227766 Simplifying p = 4.16227766Subproblem 2
p + -1 = -3.16227766 Simplifying p + -1 = -3.16227766 Reorder the terms: -1 + p = -3.16227766 Solving -1 + p = -3.16227766 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + p = -3.16227766 + 1 p = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 p = -2.16227766 Simplifying p = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.16227766, -2.16227766}
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