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Simplifying p[0.5p + 3] = 21 Reorder the terms: p[3 + 0.5p] = 21 [3 * p + 0.5p * p] = 21 [3p + 0.5p2] = 21 Solving 3p + 0.5p2 = 21 Solving for variable 'p'. Reorder the terms: -21 + 3p + 0.5p2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 3p + 0.5p2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -42 + 6p + p2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 6p + 42 + p2 = 0 + 42 Reorder the terms: -42 + 42 + 6p + p2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 6p + p2 = 0 + 42 6p + p2 = 0 + 42 Combine like terms: 0 + 42 = 42 6p + p2 = 42 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 42 + 9 Reorder the terms: 9 + 6p + p2 = 42 + 9 Combine like terms: 42 + 9 = 51 9 + 6p + p2 = 51 Factor a perfect square on the left side: (p + 3)(p + 3) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (p + 3) equal to 7.141428429 and -7.141428429.Subproblem 1
p + 3 = 7.141428429 Simplifying p + 3 = 7.141428429 Reorder the terms: 3 + p = 7.141428429 Solving 3 + p = 7.141428429 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 7.141428429 + -3 Combine like terms: 3 + -3 = 0 0 + p = 7.141428429 + -3 p = 7.141428429 + -3 Combine like terms: 7.141428429 + -3 = 4.141428429 p = 4.141428429 Simplifying p = 4.141428429Subproblem 2
p + 3 = -7.141428429 Simplifying p + 3 = -7.141428429 Reorder the terms: 3 + p = -7.141428429 Solving 3 + p = -7.141428429 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -7.141428429 + -3 Combine like terms: 3 + -3 = 0 0 + p = -7.141428429 + -3 p = -7.141428429 + -3 Combine like terms: -7.141428429 + -3 = -10.141428429 p = -10.141428429 Simplifying p = -10.141428429Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.141428429, -10.141428429}
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