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Simplifying p2 = 14p + 49 Reorder the terms: p2 = 49 + 14p Solving p2 = 49 + 14p Solving for variable 'p'. Reorder the terms: -49 + -14p + p2 = 49 + 14p + -49 + -14p Reorder the terms: -49 + -14p + p2 = 49 + -49 + 14p + -14p Combine like terms: 49 + -49 = 0 -49 + -14p + p2 = 0 + 14p + -14p -49 + -14p + p2 = 14p + -14p Combine like terms: 14p + -14p = 0 -49 + -14p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -14p + 49 + p2 = 0 + 49 Reorder the terms: -49 + 49 + -14p + p2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -14p + p2 = 0 + 49 -14p + p2 = 0 + 49 Combine like terms: 0 + 49 = 49 -14p + p2 = 49 The p term is -14p. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14p + 49 + p2 = 49 + 49 Reorder the terms: 49 + -14p + p2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + -14p + p2 = 98 Factor a perfect square on the left side: (p + -7)(p + -7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (p + -7) equal to 9.899494937 and -9.899494937.Subproblem 1
p + -7 = 9.899494937 Simplifying p + -7 = 9.899494937 Reorder the terms: -7 + p = 9.899494937 Solving -7 + p = 9.899494937 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = 9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + p = 9.899494937 + 7 p = 9.899494937 + 7 Combine like terms: 9.899494937 + 7 = 16.899494937 p = 16.899494937 Simplifying p = 16.899494937Subproblem 2
p + -7 = -9.899494937 Simplifying p + -7 = -9.899494937 Reorder the terms: -7 + p = -9.899494937 Solving -7 + p = -9.899494937 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = -9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + p = -9.899494937 + 7 p = -9.899494937 + 7 Combine like terms: -9.899494937 + 7 = -2.899494937 p = -2.899494937 Simplifying p = -2.899494937Solution
The solution to the problem is based on the solutions from the subproblems. p = {16.899494937, -2.899494937}
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