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Simplifying 9p2 + -5p + -19 = p Reorder the terms: -19 + -5p + 9p2 = p Solving -19 + -5p + 9p2 = p Solving for variable 'p'. Reorder the terms: -19 + -5p + -1p + 9p2 = p + -1p Combine like terms: -5p + -1p = -6p -19 + -6p + 9p2 = p + -1p Combine like terms: p + -1p = 0 -19 + -6p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.111111111 + -0.6666666667p + p2 = 0 Move the constant term to the right: Add '2.111111111' to each side of the equation. -2.111111111 + -0.6666666667p + 2.111111111 + p2 = 0 + 2.111111111 Reorder the terms: -2.111111111 + 2.111111111 + -0.6666666667p + p2 = 0 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + -0.6666666667p + p2 = 0 + 2.111111111 -0.6666666667p + p2 = 0 + 2.111111111 Combine like terms: 0 + 2.111111111 = 2.111111111 -0.6666666667p + p2 = 2.111111111 The p term is -0.6666666667p. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667p + 0.1111111112 + p2 = 2.111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667p + p2 = 2.111111111 + 0.1111111112 Combine like terms: 2.111111111 + 0.1111111112 = 2.2222222222 0.1111111112 + -0.6666666667p + p2 = 2.2222222222 Factor a perfect square on the left side: (p + -0.3333333334)(p + -0.3333333334) = 2.2222222222 Calculate the square root of the right side: 1.490711985 Break this problem into two subproblems by setting (p + -0.3333333334) equal to 1.490711985 and -1.490711985.Subproblem 1
p + -0.3333333334 = 1.490711985 Simplifying p + -0.3333333334 = 1.490711985 Reorder the terms: -0.3333333334 + p = 1.490711985 Solving -0.3333333334 + p = 1.490711985 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + p = 1.490711985 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + p = 1.490711985 + 0.3333333334 p = 1.490711985 + 0.3333333334 Combine like terms: 1.490711985 + 0.3333333334 = 1.8240453184 p = 1.8240453184 Simplifying p = 1.8240453184Subproblem 2
p + -0.3333333334 = -1.490711985 Simplifying p + -0.3333333334 = -1.490711985 Reorder the terms: -0.3333333334 + p = -1.490711985 Solving -0.3333333334 + p = -1.490711985 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + p = -1.490711985 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + p = -1.490711985 + 0.3333333334 p = -1.490711985 + 0.3333333334 Combine like terms: -1.490711985 + 0.3333333334 = -1.1573786516 p = -1.1573786516 Simplifying p = -1.1573786516Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.8240453184, -1.1573786516}
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