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Simplifying p2 + 10p = 7 Reorder the terms: 10p + p2 = 7 Solving 10p + p2 = 7 Solving for variable 'p'. Reorder the terms: -7 + 10p + p2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 10p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 10p + 7 + p2 = 0 + 7 Reorder the terms: -7 + 7 + 10p + p2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 10p + p2 = 0 + 7 10p + p2 = 0 + 7 Combine like terms: 0 + 7 = 7 10p + p2 = 7 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 = 7 + 25 Reorder the terms: 25 + 10p + p2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + 10p + p2 = 32 Factor a perfect square on the left side: (p + 5)(p + 5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (p + 5) equal to 5.656854249 and -5.656854249.Subproblem 1
p + 5 = 5.656854249 Simplifying p + 5 = 5.656854249 Reorder the terms: 5 + p = 5.656854249 Solving 5 + p = 5.656854249 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 = 5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + p = 5.656854249 + -5 p = 5.656854249 + -5 Combine like terms: 5.656854249 + -5 = 0.656854249 p = 0.656854249 Simplifying p = 0.656854249Subproblem 2
p + 5 = -5.656854249 Simplifying p + 5 = -5.656854249 Reorder the terms: 5 + p = -5.656854249 Solving 5 + p = -5.656854249 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 = -5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + p = -5.656854249 + -5 p = -5.656854249 + -5 Combine like terms: -5.656854249 + -5 = -10.656854249 p = -10.656854249 Simplifying p = -10.656854249Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.656854249, -10.656854249}
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