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Simplifying 49(p + -1) = p(p + 35) Reorder the terms: 49(-1 + p) = p(p + 35) (-1 * 49 + p * 49) = p(p + 35) (-49 + 49p) = p(p + 35) Reorder the terms: -49 + 49p = p(35 + p) -49 + 49p = (35 * p + p * p) -49 + 49p = (35p + p2) Solving -49 + 49p = 35p + p2 Solving for variable 'p'. Combine like terms: 49p + -35p = 14p -49 + 14p + -1p2 = 35p + p2 + -35p + -1p2 Reorder the terms: -49 + 14p + -1p2 = 35p + -35p + p2 + -1p2 Combine like terms: 35p + -35p = 0 -49 + 14p + -1p2 = 0 + p2 + -1p2 -49 + 14p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -49 + 14p + -1p2 = 0 Factor a trinomial. (-7 + p)(7 + -1p) = 0Subproblem 1
Set the factor '(-7 + p)' equal to zero and attempt to solve: Simplifying -7 + p = 0 Solving -7 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + p = 0 + 7 p = 0 + 7 Combine like terms: 0 + 7 = 7 p = 7 Simplifying p = 7Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {7, 7}
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