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Simplifying p2 + -10p + 14 = 0 Reorder the terms: 14 + -10p + p2 = 0 Solving 14 + -10p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -10p + -14 + p2 = 0 + -14 Reorder the terms: 14 + -14 + -10p + p2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -10p + p2 = 0 + -14 -10p + p2 = 0 + -14 Combine like terms: 0 + -14 = -14 -10p + p2 = -14 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 = -14 + 25 Reorder the terms: 25 + -10p + p2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + -10p + p2 = 11 Factor a perfect square on the left side: (p + -5)(p + -5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (p + -5) equal to 3.31662479 and -3.31662479.Subproblem 1
p + -5 = 3.31662479 Simplifying p + -5 = 3.31662479 Reorder the terms: -5 + p = 3.31662479 Solving -5 + p = 3.31662479 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 = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + p = 3.31662479 + 5 p = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 p = 8.31662479 Simplifying p = 8.31662479Subproblem 2
p + -5 = -3.31662479 Simplifying p + -5 = -3.31662479 Reorder the terms: -5 + p = -3.31662479 Solving -5 + p = -3.31662479 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 = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + p = -3.31662479 + 5 p = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 p = 1.68337521 Simplifying p = 1.68337521Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.31662479, 1.68337521}
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