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Simplifying p2 + -14p + 4 = 0 Reorder the terms: 4 + -14p + p2 = 0 Solving 4 + -14p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -14p + -4 + p2 = 0 + -4 Reorder the terms: 4 + -4 + -14p + p2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -14p + p2 = 0 + -4 -14p + p2 = 0 + -4 Combine like terms: 0 + -4 = -4 -14p + p2 = -4 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 = -4 + 49 Reorder the terms: 49 + -14p + p2 = -4 + 49 Combine like terms: -4 + 49 = 45 49 + -14p + p2 = 45 Factor a perfect square on the left side: (p + -7)(p + -7) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (p + -7) equal to 6.708203933 and -6.708203933.Subproblem 1
p + -7 = 6.708203933 Simplifying p + -7 = 6.708203933 Reorder the terms: -7 + p = 6.708203933 Solving -7 + p = 6.708203933 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 = 6.708203933 + 7 Combine like terms: -7 + 7 = 0 0 + p = 6.708203933 + 7 p = 6.708203933 + 7 Combine like terms: 6.708203933 + 7 = 13.708203933 p = 13.708203933 Simplifying p = 13.708203933Subproblem 2
p + -7 = -6.708203933 Simplifying p + -7 = -6.708203933 Reorder the terms: -7 + p = -6.708203933 Solving -7 + p = -6.708203933 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 = -6.708203933 + 7 Combine like terms: -7 + 7 = 0 0 + p = -6.708203933 + 7 p = -6.708203933 + 7 Combine like terms: -6.708203933 + 7 = 0.291796067 p = 0.291796067 Simplifying p = 0.291796067Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.708203933, 0.291796067}
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