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Simplifying 9p2 = 3p + 9 Reorder the terms: 9p2 = 9 + 3p Solving 9p2 = 9 + 3p Solving for variable 'p'. Reorder the terms: -9 + -3p + 9p2 = 9 + 3p + -9 + -3p Reorder the terms: -9 + -3p + 9p2 = 9 + -9 + 3p + -3p Combine like terms: 9 + -9 = 0 -9 + -3p + 9p2 = 0 + 3p + -3p -9 + -3p + 9p2 = 3p + -3p Combine like terms: 3p + -3p = 0 -9 + -3p + 9p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -1p + 3p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1p + 3p2)' equal to zero and attempt to solve: Simplifying -3 + -1p + 3p2 = 0 Solving -3 + -1p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -0.3333333333p + p2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.3333333333p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + -0.3333333333p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.3333333333p + p2 = 0 + 1 -0.3333333333p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.3333333333p + p2 = 1 The p term is -0.3333333333p. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333p + 0.02777777779 + p2 = 1 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333p + p2 = 1 + 0.02777777779 Combine like terms: 1 + 0.02777777779 = 1.02777777779 0.02777777779 + -0.3333333333p + p2 = 1.02777777779 Factor a perfect square on the left side: (p + -0.1666666667)(p + -0.1666666667) = 1.02777777779 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (p + -0.1666666667) equal to 1.013793755 and -1.013793755.Subproblem 1
p + -0.1666666667 = 1.013793755 Simplifying p + -0.1666666667 = 1.013793755 Reorder the terms: -0.1666666667 + p = 1.013793755 Solving -0.1666666667 + p = 1.013793755 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + p = 1.013793755 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + p = 1.013793755 + 0.1666666667 p = 1.013793755 + 0.1666666667 Combine like terms: 1.013793755 + 0.1666666667 = 1.1804604217 p = 1.1804604217 Simplifying p = 1.1804604217Subproblem 2
p + -0.1666666667 = -1.013793755 Simplifying p + -0.1666666667 = -1.013793755 Reorder the terms: -0.1666666667 + p = -1.013793755 Solving -0.1666666667 + p = -1.013793755 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + p = -1.013793755 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + p = -1.013793755 + 0.1666666667 p = -1.013793755 + 0.1666666667 Combine like terms: -1.013793755 + 0.1666666667 = -0.8471270883 p = -0.8471270883 Simplifying p = -0.8471270883Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.1804604217, -0.8471270883}Solution
p = {1.1804604217, -0.8471270883}
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