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Simplifying p2 + 10p + -4 = 0 Reorder the terms: -4 + 10p + p2 = 0 Solving -4 + 10p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 10p + 4 + p2 = 0 + 4 Reorder the terms: -4 + 4 + 10p + p2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 10p + p2 = 0 + 4 10p + p2 = 0 + 4 Combine like terms: 0 + 4 = 4 10p + p2 = 4 The p term is 10p. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10p + 25 + p2 = 4 + 25 Reorder the terms: 25 + 10p + p2 = 4 + 25 Combine like terms: 4 + 25 = 29 25 + 10p + p2 = 29 Factor a perfect square on the left side: (p + 5)(p + 5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (p + 5) equal to 5.385164807 and -5.385164807.Subproblem 1
p + 5 = 5.385164807 Simplifying p + 5 = 5.385164807 Reorder the terms: 5 + p = 5.385164807 Solving 5 + p = 5.385164807 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 5.385164807 + -5 Combine like terms: 5 + -5 = 0 0 + p = 5.385164807 + -5 p = 5.385164807 + -5 Combine like terms: 5.385164807 + -5 = 0.385164807 p = 0.385164807 Simplifying p = 0.385164807Subproblem 2
p + 5 = -5.385164807 Simplifying p + 5 = -5.385164807 Reorder the terms: 5 + p = -5.385164807 Solving 5 + p = -5.385164807 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -5.385164807 + -5 Combine like terms: 5 + -5 = 0 0 + p = -5.385164807 + -5 p = -5.385164807 + -5 Combine like terms: -5.385164807 + -5 = -10.385164807 p = -10.385164807 Simplifying p = -10.385164807Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.385164807, -10.385164807}
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