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Simplifying 3p2 + 12p + -25 = 0 Reorder the terms: -25 + 12p + 3p2 = 0 Solving -25 + 12p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.333333333 + 4p + p2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + 4p + 8.333333333 + p2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + 4p + p2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + 4p + p2 = 0 + 8.333333333 4p + p2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 4p + p2 = 8.333333333 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 8.333333333 + 4 Reorder the terms: 4 + 4p + p2 = 8.333333333 + 4 Combine like terms: 8.333333333 + 4 = 12.333333333 4 + 4p + p2 = 12.333333333 Factor a perfect square on the left side: (p + 2)(p + 2) = 12.333333333 Calculate the square root of the right side: 3.511884584 Break this problem into two subproblems by setting (p + 2) equal to 3.511884584 and -3.511884584.Subproblem 1
p + 2 = 3.511884584 Simplifying p + 2 = 3.511884584 Reorder the terms: 2 + p = 3.511884584 Solving 2 + p = 3.511884584 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 3.511884584 + -2 Combine like terms: 2 + -2 = 0 0 + p = 3.511884584 + -2 p = 3.511884584 + -2 Combine like terms: 3.511884584 + -2 = 1.511884584 p = 1.511884584 Simplifying p = 1.511884584Subproblem 2
p + 2 = -3.511884584 Simplifying p + 2 = -3.511884584 Reorder the terms: 2 + p = -3.511884584 Solving 2 + p = -3.511884584 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -3.511884584 + -2 Combine like terms: 2 + -2 = 0 0 + p = -3.511884584 + -2 p = -3.511884584 + -2 Combine like terms: -3.511884584 + -2 = -5.511884584 p = -5.511884584 Simplifying p = -5.511884584Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.511884584, -5.511884584}
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