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Simplifying 12 + -24p + -4p2 = 0 Solving 12 + -24p + -4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -6p + -1p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -6p + -1p2)' equal to zero and attempt to solve: Simplifying 3 + -6p + -1p2 = 0 Solving 3 + -6p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 6p + p2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6p + 3 + p2 = 0 + 3 Reorder the terms: -3 + 3 + 6p + p2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6p + p2 = 0 + 3 6p + p2 = 0 + 3 Combine like terms: 0 + 3 = 3 6p + p2 = 3 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 = 3 + 9 Reorder the terms: 9 + 6p + p2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6p + p2 = 12 Factor a perfect square on the left side: (p + 3)(p + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (p + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
p + 3 = 3.464101615 Simplifying p + 3 = 3.464101615 Reorder the terms: 3 + p = 3.464101615 Solving 3 + p = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.464101615 + -3 p = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 p = 0.464101615 Simplifying p = 0.464101615Subproblem 2
p + 3 = -3.464101615 Simplifying p + 3 = -3.464101615 Reorder the terms: 3 + p = -3.464101615 Solving 3 + p = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.464101615 + -3 p = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 p = -6.464101615 Simplifying p = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.464101615, -6.464101615}Solution
p = {0.464101615, -6.464101615}
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