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Simplifying 6p(5p + 5) = -8 + -2(p + 12) Reorder the terms: 6p(5 + 5p) = -8 + -2(p + 12) (5 * 6p + 5p * 6p) = -8 + -2(p + 12) (30p + 30p2) = -8 + -2(p + 12) Reorder the terms: 30p + 30p2 = -8 + -2(12 + p) 30p + 30p2 = -8 + (12 * -2 + p * -2) 30p + 30p2 = -8 + (-24 + -2p) Combine like terms: -8 + -24 = -32 30p + 30p2 = -32 + -2p Solving 30p + 30p2 = -32 + -2p Solving for variable 'p'. Reorder the terms: 32 + 30p + 2p + 30p2 = -32 + -2p + 32 + 2p Combine like terms: 30p + 2p = 32p 32 + 32p + 30p2 = -32 + -2p + 32 + 2p Reorder the terms: 32 + 32p + 30p2 = -32 + 32 + -2p + 2p Combine like terms: -32 + 32 = 0 32 + 32p + 30p2 = 0 + -2p + 2p 32 + 32p + 30p2 = -2p + 2p Combine like terms: -2p + 2p = 0 32 + 32p + 30p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 16p + 15p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + 16p + 15p2)' equal to zero and attempt to solve: Simplifying 16 + 16p + 15p2 = 0 Solving 16 + 16p + 15p2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.066666667 + 1.066666667p + p2 = 0 Move the constant term to the right: Add '-1.066666667' to each side of the equation. 1.066666667 + 1.066666667p + -1.066666667 + p2 = 0 + -1.066666667 Reorder the terms: 1.066666667 + -1.066666667 + 1.066666667p + p2 = 0 + -1.066666667 Combine like terms: 1.066666667 + -1.066666667 = 0.000000000 0.000000000 + 1.066666667p + p2 = 0 + -1.066666667 1.066666667p + p2 = 0 + -1.066666667 Combine like terms: 0 + -1.066666667 = -1.066666667 1.066666667p + p2 = -1.066666667 The p term is 1.066666667p. Take half its coefficient (0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. 1.066666667p + 0.2844444446 + p2 = -1.066666667 + 0.2844444446 Reorder the terms: 0.2844444446 + 1.066666667p + p2 = -1.066666667 + 0.2844444446 Combine like terms: -1.066666667 + 0.2844444446 = -0.7822222224 0.2844444446 + 1.066666667p + p2 = -0.7822222224 Factor a perfect square on the left side: (p + 0.5333333335)(p + 0.5333333335) = -0.7822222224 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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