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Simplifying -1p2 + 4p + 8 = 0 Reorder the terms: 8 + 4p + -1p2 = 0 Solving 8 + 4p + -1p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -4p + p2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -4p + 8 + p2 = 0 + 8 Reorder the terms: -8 + 8 + -4p + p2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4p + p2 = 0 + 8 -4p + p2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4p + p2 = 8 The p term is -4p. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4p + 4 + p2 = 8 + 4 Reorder the terms: 4 + -4p + p2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4p + p2 = 12 Factor a perfect square on the left side: (p + -2)(p + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (p + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
p + -2 = 3.464101615 Simplifying p + -2 = 3.464101615 Reorder the terms: -2 + p = 3.464101615 Solving -2 + p = 3.464101615 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + p = 3.464101615 + 2 p = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 p = 5.464101615 Simplifying p = 5.464101615Subproblem 2
p + -2 = -3.464101615 Simplifying p + -2 = -3.464101615 Reorder the terms: -2 + p = -3.464101615 Solving -2 + p = -3.464101615 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + p = -3.464101615 + 2 p = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 p = -1.464101615 Simplifying p = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.464101615, -1.464101615}
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