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Simplifying (p + 5)(p + 5) + -49 = 0 Reorder the terms: (5 + p)(p + 5) + -49 = 0 Reorder the terms: (5 + p)(5 + p) + -49 = 0 Multiply (5 + p) * (5 + p) (5(5 + p) + p(5 + p)) + -49 = 0 ((5 * 5 + p * 5) + p(5 + p)) + -49 = 0 ((25 + 5p) + p(5 + p)) + -49 = 0 (25 + 5p + (5 * p + p * p)) + -49 = 0 (25 + 5p + (5p + p2)) + -49 = 0 Combine like terms: 5p + 5p = 10p (25 + 10p + p2) + -49 = 0 Reorder the terms: 25 + -49 + 10p + p2 = 0 Combine like terms: 25 + -49 = -24 -24 + 10p + p2 = 0 Solving -24 + 10p + p2 = 0 Solving for variable 'p'. Factor a trinomial. (-12 + -1p)(2 + -1p) = 0Subproblem 1
Set the factor '(-12 + -1p)' equal to zero and attempt to solve: Simplifying -12 + -1p = 0 Solving -12 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1p = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1p = 0 + 12 -1p = 0 + 12 Combine like terms: 0 + 12 = 12 -1p = 12 Divide each side by '-1'. p = -12 Simplifying p = -12Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {-12, 2}
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