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Simplifying p * p + -14p + 18 = 0 Multiply p * p p2 + -14p + 18 = 0 Reorder the terms: 18 + -14p + p2 = 0 Solving 18 + -14p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -14p + -18 + p2 = 0 + -18 Reorder the terms: 18 + -18 + -14p + p2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -14p + p2 = 0 + -18 -14p + p2 = 0 + -18 Combine like terms: 0 + -18 = -18 -14p + p2 = -18 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 = -18 + 49 Reorder the terms: 49 + -14p + p2 = -18 + 49 Combine like terms: -18 + 49 = 31 49 + -14p + p2 = 31 Factor a perfect square on the left side: (p + -7)(p + -7) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (p + -7) equal to 5.567764363 and -5.567764363.Subproblem 1
p + -7 = 5.567764363 Simplifying p + -7 = 5.567764363 Reorder the terms: -7 + p = 5.567764363 Solving -7 + p = 5.567764363 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 = 5.567764363 + 7 Combine like terms: -7 + 7 = 0 0 + p = 5.567764363 + 7 p = 5.567764363 + 7 Combine like terms: 5.567764363 + 7 = 12.567764363 p = 12.567764363 Simplifying p = 12.567764363Subproblem 2
p + -7 = -5.567764363 Simplifying p + -7 = -5.567764363 Reorder the terms: -7 + p = -5.567764363 Solving -7 + p = -5.567764363 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 = -5.567764363 + 7 Combine like terms: -7 + 7 = 0 0 + p = -5.567764363 + 7 p = -5.567764363 + 7 Combine like terms: -5.567764363 + 7 = 1.432235637 p = 1.432235637 Simplifying p = 1.432235637Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.567764363, 1.432235637}
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