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Simplifying p2 + -9p + 6 = 0 Reorder the terms: 6 + -9p + p2 = 0 Solving 6 + -9p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -9p + -6 + p2 = 0 + -6 Reorder the terms: 6 + -6 + -9p + p2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9p + p2 = 0 + -6 -9p + p2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9p + p2 = -6 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = -6 + 20.25 Reorder the terms: 20.25 + -9p + p2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + -9p + p2 = 14.25 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (p + -4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
p + -4.5 = 3.774917218 Simplifying p + -4.5 = 3.774917218 Reorder the terms: -4.5 + p = 3.774917218 Solving -4.5 + p = 3.774917218 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 3.774917218 + 4.5 p = 3.774917218 + 4.5 Combine like terms: 3.774917218 + 4.5 = 8.274917218 p = 8.274917218 Simplifying p = 8.274917218Subproblem 2
p + -4.5 = -3.774917218 Simplifying p + -4.5 = -3.774917218 Reorder the terms: -4.5 + p = -3.774917218 Solving -4.5 + p = -3.774917218 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -3.774917218 + 4.5 p = -3.774917218 + 4.5 Combine like terms: -3.774917218 + 4.5 = 0.725082782 p = 0.725082782 Simplifying p = 0.725082782Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.274917218, 0.725082782}
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