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Simplifying p2 + -15p + 30 = 0 Reorder the terms: 30 + -15p + p2 = 0 Solving 30 + -15p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -15p + -30 + p2 = 0 + -30 Reorder the terms: 30 + -30 + -15p + p2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -15p + p2 = 0 + -30 -15p + p2 = 0 + -30 Combine like terms: 0 + -30 = -30 -15p + p2 = -30 The p term is -15p. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15p + 56.25 + p2 = -30 + 56.25 Reorder the terms: 56.25 + -15p + p2 = -30 + 56.25 Combine like terms: -30 + 56.25 = 26.25 56.25 + -15p + p2 = 26.25 Factor a perfect square on the left side: (p + -7.5)(p + -7.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (p + -7.5) equal to 5.123475383 and -5.123475383.Subproblem 1
p + -7.5 = 5.123475383 Simplifying p + -7.5 = 5.123475383 Reorder the terms: -7.5 + p = 5.123475383 Solving -7.5 + p = 5.123475383 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + p = 5.123475383 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + p = 5.123475383 + 7.5 p = 5.123475383 + 7.5 Combine like terms: 5.123475383 + 7.5 = 12.623475383 p = 12.623475383 Simplifying p = 12.623475383Subproblem 2
p + -7.5 = -5.123475383 Simplifying p + -7.5 = -5.123475383 Reorder the terms: -7.5 + p = -5.123475383 Solving -7.5 + p = -5.123475383 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + p = -5.123475383 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + p = -5.123475383 + 7.5 p = -5.123475383 + 7.5 Combine like terms: -5.123475383 + 7.5 = 2.376524617 p = 2.376524617 Simplifying p = 2.376524617Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.623475383, 2.376524617}
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