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Simplifying -33 + -7p = -5(6p + -5) * 6p Reorder the terms: -33 + -7p = -5(-5 + 6p) * 6p Reorder the terms for easier multiplication: -33 + -7p = -5 * 6p(-5 + 6p) Multiply -5 * 6 -33 + -7p = -30p(-5 + 6p) -33 + -7p = (-5 * -30p + 6p * -30p) -33 + -7p = (150p + -180p2) Solving -33 + -7p = 150p + -180p2 Solving for variable 'p'. Combine like terms: -7p + -150p = -157p -33 + -157p + 180p2 = 150p + -180p2 + -150p + 180p2 Reorder the terms: -33 + -157p + 180p2 = 150p + -150p + -180p2 + 180p2 Combine like terms: 150p + -150p = 0 -33 + -157p + 180p2 = 0 + -180p2 + 180p2 -33 + -157p + 180p2 = -180p2 + 180p2 Combine like terms: -180p2 + 180p2 = 0 -33 + -157p + 180p2 = 0 Begin completing the square. Divide all terms by 180 the coefficient of the squared term: Divide each side by '180'. -0.1833333333 + -0.8722222222p + p2 = 0 Move the constant term to the right: Add '0.1833333333' to each side of the equation. -0.1833333333 + -0.8722222222p + 0.1833333333 + p2 = 0 + 0.1833333333 Reorder the terms: -0.1833333333 + 0.1833333333 + -0.8722222222p + p2 = 0 + 0.1833333333 Combine like terms: -0.1833333333 + 0.1833333333 = 0.0000000000 0.0000000000 + -0.8722222222p + p2 = 0 + 0.1833333333 -0.8722222222p + p2 = 0 + 0.1833333333 Combine like terms: 0 + 0.1833333333 = 0.1833333333 -0.8722222222p + p2 = 0.1833333333 The p term is -0.8722222222p. Take half its coefficient (-0.4361111111). Square it (0.1901929012) and add it to both sides. Add '0.1901929012' to each side of the equation. -0.8722222222p + 0.1901929012 + p2 = 0.1833333333 + 0.1901929012 Reorder the terms: 0.1901929012 + -0.8722222222p + p2 = 0.1833333333 + 0.1901929012 Combine like terms: 0.1833333333 + 0.1901929012 = 0.3735262345 0.1901929012 + -0.8722222222p + p2 = 0.3735262345 Factor a perfect square on the left side: (p + -0.4361111111)(p + -0.4361111111) = 0.3735262345 Calculate the square root of the right side: 0.611167927 Break this problem into two subproblems by setting (p + -0.4361111111) equal to 0.611167927 and -0.611167927.Subproblem 1
p + -0.4361111111 = 0.611167927 Simplifying p + -0.4361111111 = 0.611167927 Reorder the terms: -0.4361111111 + p = 0.611167927 Solving -0.4361111111 + p = 0.611167927 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4361111111' to each side of the equation. -0.4361111111 + 0.4361111111 + p = 0.611167927 + 0.4361111111 Combine like terms: -0.4361111111 + 0.4361111111 = 0.0000000000 0.0000000000 + p = 0.611167927 + 0.4361111111 p = 0.611167927 + 0.4361111111 Combine like terms: 0.611167927 + 0.4361111111 = 1.0472790381 p = 1.0472790381 Simplifying p = 1.0472790381Subproblem 2
p + -0.4361111111 = -0.611167927 Simplifying p + -0.4361111111 = -0.611167927 Reorder the terms: -0.4361111111 + p = -0.611167927 Solving -0.4361111111 + p = -0.611167927 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4361111111' to each side of the equation. -0.4361111111 + 0.4361111111 + p = -0.611167927 + 0.4361111111 Combine like terms: -0.4361111111 + 0.4361111111 = 0.0000000000 0.0000000000 + p = -0.611167927 + 0.4361111111 p = -0.611167927 + 0.4361111111 Combine like terms: -0.611167927 + 0.4361111111 = -0.1750568159 p = -0.1750568159 Simplifying p = -0.1750568159Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.0472790381, -0.1750568159}
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