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Simplifying 7p + -2p(3 + -4p) = 12p + -1(5p + 4) 7p + (3 * -2p + -4p * -2p) = 12p + -1(5p + 4) 7p + (-6p + 8p2) = 12p + -1(5p + 4) Combine like terms: 7p + -6p = 1p 1p + 8p2 = 12p + -1(5p + 4) Reorder the terms: 1p + 8p2 = 12p + -1(4 + 5p) 1p + 8p2 = 12p + (4 * -1 + 5p * -1) 1p + 8p2 = 12p + (-4 + -5p) Reorder the terms: 1p + 8p2 = -4 + 12p + -5p Combine like terms: 12p + -5p = 7p 1p + 8p2 = -4 + 7p Solving 1p + 8p2 = -4 + 7p Solving for variable 'p'. Reorder the terms: 4 + 1p + -7p + 8p2 = -4 + 7p + 4 + -7p Combine like terms: 1p + -7p = -6p 4 + -6p + 8p2 = -4 + 7p + 4 + -7p Reorder the terms: 4 + -6p + 8p2 = -4 + 4 + 7p + -7p Combine like terms: -4 + 4 = 0 4 + -6p + 8p2 = 0 + 7p + -7p 4 + -6p + 8p2 = 7p + -7p Combine like terms: 7p + -7p = 0 4 + -6p + 8p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -3p + 4p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3p + 4p2)' equal to zero and attempt to solve: Simplifying 2 + -3p + 4p2 = 0 Solving 2 + -3p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -0.75p + p2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.75p + -0.5 + p2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.75p + p2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.75p + p2 = 0 + -0.5 -0.75p + p2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.75p + p2 = -0.5 The p term is -0.75p. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75p + 0.140625 + p2 = -0.5 + 0.140625 Reorder the terms: 0.140625 + -0.75p + p2 = -0.5 + 0.140625 Combine like terms: -0.5 + 0.140625 = -0.359375 0.140625 + -0.75p + p2 = -0.359375 Factor a perfect square on the left side: (p + -0.375)(p + -0.375) = -0.359375 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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