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Simplifying 3p2 + 3p + -15 = 0 Reorder the terms: -15 + 3p + 3p2 = 0 Solving -15 + 3p + 3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + p + p2)' equal to zero and attempt to solve: Simplifying -5 + p + p2 = 0 Solving -5 + p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + p + p2 = 0 + 5 p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 p + p2 = 5 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. p + 0.25 + p2 = 5 + 0.25 Reorder the terms: 0.25 + p + p2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + p + p2 = 5.25 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (p + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
p + 0.5 = 2.291287847 Simplifying p + 0.5 = 2.291287847 Reorder the terms: 0.5 + p = 2.291287847 Solving 0.5 + p = 2.291287847 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 2.291287847 + -0.5 p = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 p = 1.791287847 Simplifying p = 1.791287847Subproblem 2
p + 0.5 = -2.291287847 Simplifying p + 0.5 = -2.291287847 Reorder the terms: 0.5 + p = -2.291287847 Solving 0.5 + p = -2.291287847 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -2.291287847 + -0.5 p = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 p = -2.791287847 Simplifying p = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.791287847, -2.791287847}Solution
p = {1.791287847, -2.791287847}
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