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Simplifying 2p2 + -12p + -2 = 0 Reorder the terms: -2 + -12p + 2p2 = 0 Solving -2 + -12p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -6p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -6p + p2)' equal to zero and attempt to solve: Simplifying -1 + -6p + p2 = 0 Solving -1 + -6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -6p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + -6p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6p + p2 = 0 + 1 -6p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6p + p2 = 1 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 = 1 + 9 Reorder the terms: 9 + -6p + p2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6p + p2 = 10 Factor a perfect square on the left side: (p + -3)(p + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (p + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
p + -3 = 3.16227766 Simplifying p + -3 = 3.16227766 Reorder the terms: -3 + p = 3.16227766 Solving -3 + p = 3.16227766 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 = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + p = 3.16227766 + 3 p = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 p = 6.16227766 Simplifying p = 6.16227766Subproblem 2
p + -3 = -3.16227766 Simplifying p + -3 = -3.16227766 Reorder the terms: -3 + p = -3.16227766 Solving -3 + p = -3.16227766 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 = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + p = -3.16227766 + 3 p = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 p = -0.16227766 Simplifying p = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.16227766, -0.16227766}Solution
p = {6.16227766, -0.16227766}
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