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Simplifying 5p2 + -6p + -23 = 0 Reorder the terms: -23 + -6p + 5p2 = 0 Solving -23 + -6p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.6 + -1.2p + p2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + -1.2p + 4.6 + p2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + -1.2p + p2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + -1.2p + p2 = 0 + 4.6 -1.2p + p2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 -1.2p + p2 = 4.6 The p term is -1.2p. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2p + 0.36 + p2 = 4.6 + 0.36 Reorder the terms: 0.36 + -1.2p + p2 = 4.6 + 0.36 Combine like terms: 4.6 + 0.36 = 4.96 0.36 + -1.2p + p2 = 4.96 Factor a perfect square on the left side: (p + -0.6)(p + -0.6) = 4.96 Calculate the square root of the right side: 2.227105745 Break this problem into two subproblems by setting (p + -0.6) equal to 2.227105745 and -2.227105745.Subproblem 1
p + -0.6 = 2.227105745 Simplifying p + -0.6 = 2.227105745 Reorder the terms: -0.6 + p = 2.227105745 Solving -0.6 + p = 2.227105745 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + p = 2.227105745 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + p = 2.227105745 + 0.6 p = 2.227105745 + 0.6 Combine like terms: 2.227105745 + 0.6 = 2.827105745 p = 2.827105745 Simplifying p = 2.827105745Subproblem 2
p + -0.6 = -2.227105745 Simplifying p + -0.6 = -2.227105745 Reorder the terms: -0.6 + p = -2.227105745 Solving -0.6 + p = -2.227105745 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + p = -2.227105745 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + p = -2.227105745 + 0.6 p = -2.227105745 + 0.6 Combine like terms: -2.227105745 + 0.6 = -1.627105745 p = -1.627105745 Simplifying p = -1.627105745Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.827105745, -1.627105745}
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