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Simplifying p2 + -13p + 18 = 0 Reorder the terms: 18 + -13p + p2 = 0 Solving 18 + -13p + 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 + -13p + -18 + p2 = 0 + -18 Reorder the terms: 18 + -18 + -13p + p2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -13p + p2 = 0 + -18 -13p + p2 = 0 + -18 Combine like terms: 0 + -18 = -18 -13p + p2 = -18 The p term is -13p. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13p + 42.25 + p2 = -18 + 42.25 Reorder the terms: 42.25 + -13p + p2 = -18 + 42.25 Combine like terms: -18 + 42.25 = 24.25 42.25 + -13p + p2 = 24.25 Factor a perfect square on the left side: (p + -6.5)(p + -6.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (p + -6.5) equal to 4.924428901 and -4.924428901.Subproblem 1
p + -6.5 = 4.924428901 Simplifying p + -6.5 = 4.924428901 Reorder the terms: -6.5 + p = 4.924428901 Solving -6.5 + p = 4.924428901 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + p = 4.924428901 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + p = 4.924428901 + 6.5 p = 4.924428901 + 6.5 Combine like terms: 4.924428901 + 6.5 = 11.424428901 p = 11.424428901 Simplifying p = 11.424428901Subproblem 2
p + -6.5 = -4.924428901 Simplifying p + -6.5 = -4.924428901 Reorder the terms: -6.5 + p = -4.924428901 Solving -6.5 + p = -4.924428901 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + p = -4.924428901 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + p = -4.924428901 + 6.5 p = -4.924428901 + 6.5 Combine like terms: -4.924428901 + 6.5 = 1.575571099 p = 1.575571099 Simplifying p = 1.575571099Solution
The solution to the problem is based on the solutions from the subproblems. p = {11.424428901, 1.575571099}
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