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Simplifying p2 = 48 + 14p Solving p2 = 48 + 14p Solving for variable 'p'. Reorder the terms: -48 + -14p + p2 = 48 + 14p + -48 + -14p Reorder the terms: -48 + -14p + p2 = 48 + -48 + 14p + -14p Combine like terms: 48 + -48 = 0 -48 + -14p + p2 = 0 + 14p + -14p -48 + -14p + p2 = 14p + -14p Combine like terms: 14p + -14p = 0 -48 + -14p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -14p + 48 + p2 = 0 + 48 Reorder the terms: -48 + 48 + -14p + p2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -14p + p2 = 0 + 48 -14p + p2 = 0 + 48 Combine like terms: 0 + 48 = 48 -14p + p2 = 48 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 = 48 + 49 Reorder the terms: 49 + -14p + p2 = 48 + 49 Combine like terms: 48 + 49 = 97 49 + -14p + p2 = 97 Factor a perfect square on the left side: (p + -7)(p + -7) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (p + -7) equal to 9.848857802 and -9.848857802.Subproblem 1
p + -7 = 9.848857802 Simplifying p + -7 = 9.848857802 Reorder the terms: -7 + p = 9.848857802 Solving -7 + p = 9.848857802 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 = 9.848857802 + 7 Combine like terms: -7 + 7 = 0 0 + p = 9.848857802 + 7 p = 9.848857802 + 7 Combine like terms: 9.848857802 + 7 = 16.848857802 p = 16.848857802 Simplifying p = 16.848857802Subproblem 2
p + -7 = -9.848857802 Simplifying p + -7 = -9.848857802 Reorder the terms: -7 + p = -9.848857802 Solving -7 + p = -9.848857802 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 = -9.848857802 + 7 Combine like terms: -7 + 7 = 0 0 + p = -9.848857802 + 7 p = -9.848857802 + 7 Combine like terms: -9.848857802 + 7 = -2.848857802 p = -2.848857802 Simplifying p = -2.848857802Solution
The solution to the problem is based on the solutions from the subproblems. p = {16.848857802, -2.848857802}
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