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Simplifying -7(7 + 5p) + -1p(1 + 8p) = 0 (7 * -7 + 5p * -7) + -1p(1 + 8p) = 0 (-49 + -35p) + -1p(1 + 8p) = 0 -49 + -35p + (1 * -1p + 8p * -1p) = 0 -49 + -35p + (-1p + -8p2) = 0 Combine like terms: -35p + -1p = -36p -49 + -36p + -8p2 = 0 Solving -49 + -36p + -8p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '-1'. -1(49 + 36p + 8p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(49 + 36p + 8p2)' equal to zero and attempt to solve: Simplifying 49 + 36p + 8p2 = 0 Solving 49 + 36p + 8p2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.125 + 4.5p + p2 = 0 Move the constant term to the right: Add '-6.125' to each side of the equation. 6.125 + 4.5p + -6.125 + p2 = 0 + -6.125 Reorder the terms: 6.125 + -6.125 + 4.5p + p2 = 0 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + 4.5p + p2 = 0 + -6.125 4.5p + p2 = 0 + -6.125 Combine like terms: 0 + -6.125 = -6.125 4.5p + p2 = -6.125 The p term is 4.5p. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5p + 5.0625 + p2 = -6.125 + 5.0625 Reorder the terms: 5.0625 + 4.5p + p2 = -6.125 + 5.0625 Combine like terms: -6.125 + 5.0625 = -1.0625 5.0625 + 4.5p + p2 = -1.0625 Factor a perfect square on the left side: (p + 2.25)(p + 2.25) = -1.0625 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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