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Simplifying -1(p + 3) + p2 + 4p = 0 Reorder the terms: -1(3 + p) + p2 + 4p = 0 (3 * -1 + p * -1) + p2 + 4p = 0 (-3 + -1p) + p2 + 4p = 0 Reorder the terms: -3 + -1p + 4p + p2 = 0 Combine like terms: -1p + 4p = 3p -3 + 3p + p2 = 0 Solving -3 + 3p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 3p + 3 + p2 = 0 + 3 Reorder the terms: -3 + 3 + 3p + p2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3p + p2 = 0 + 3 3p + p2 = 0 + 3 Combine like terms: 0 + 3 = 3 3p + p2 = 3 The p term is 3p. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3p + 2.25 + p2 = 3 + 2.25 Reorder the terms: 2.25 + 3p + p2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + 3p + p2 = 5.25 Factor a perfect square on the left side: (p + 1.5)(p + 1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (p + 1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
p + 1.5 = 2.291287847 Simplifying p + 1.5 = 2.291287847 Reorder the terms: 1.5 + p = 2.291287847 Solving 1.5 + p = 2.291287847 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + p = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + p = 2.291287847 + -1.5 p = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 p = 0.791287847 Simplifying p = 0.791287847Subproblem 2
p + 1.5 = -2.291287847 Simplifying p + 1.5 = -2.291287847 Reorder the terms: 1.5 + p = -2.291287847 Solving 1.5 + p = -2.291287847 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + p = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + p = -2.291287847 + -1.5 p = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 p = -3.791287847 Simplifying p = -3.791287847Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.791287847, -3.791287847}
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