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Simplifying p + 1(p2 + 10p + 21) = 0 Reorder the terms: p + 1(21 + 10p + p2) = 0 p + (21 * 1 + 10p * 1 + p2 * 1) = 0 p + (21 + 10p + 1p2) = 0 Reorder the terms: 21 + p + 10p + 1p2 = 0 Combine like terms: p + 10p = 11p 21 + 11p + 1p2 = 0 Solving 21 + 11p + 1p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 11p + -21 + p2 = 0 + -21 Reorder the terms: 21 + -21 + 11p + p2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 11p + p2 = 0 + -21 11p + p2 = 0 + -21 Combine like terms: 0 + -21 = -21 11p + p2 = -21 The p term is 11p. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11p + 30.25 + p2 = -21 + 30.25 Reorder the terms: 30.25 + 11p + p2 = -21 + 30.25 Combine like terms: -21 + 30.25 = 9.25 30.25 + 11p + p2 = 9.25 Factor a perfect square on the left side: (p + 5.5)(p + 5.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (p + 5.5) equal to 3.041381265 and -3.041381265.Subproblem 1
p + 5.5 = 3.041381265 Simplifying p + 5.5 = 3.041381265 Reorder the terms: 5.5 + p = 3.041381265 Solving 5.5 + p = 3.041381265 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + p = 3.041381265 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = 3.041381265 + -5.5 p = 3.041381265 + -5.5 Combine like terms: 3.041381265 + -5.5 = -2.458618735 p = -2.458618735 Simplifying p = -2.458618735Subproblem 2
p + 5.5 = -3.041381265 Simplifying p + 5.5 = -3.041381265 Reorder the terms: 5.5 + p = -3.041381265 Solving 5.5 + p = -3.041381265 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + p = -3.041381265 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = -3.041381265 + -5.5 p = -3.041381265 + -5.5 Combine like terms: -3.041381265 + -5.5 = -8.541381265 p = -8.541381265 Simplifying p = -8.541381265Solution
The solution to the problem is based on the solutions from the subproblems. p = {-2.458618735, -8.541381265}
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