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Simplifying 5p2 + -10p + 119 = 24 Reorder the terms: 119 + -10p + 5p2 = 24 Solving 119 + -10p + 5p2 = 24 Solving for variable 'p'. Reorder the terms: 119 + -24 + -10p + 5p2 = 24 + -24 Combine like terms: 119 + -24 = 95 95 + -10p + 5p2 = 24 + -24 Combine like terms: 24 + -24 = 0 95 + -10p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(19 + -2p + p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(19 + -2p + p2)' equal to zero and attempt to solve: Simplifying 19 + -2p + p2 = 0 Solving 19 + -2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -2p + -19 + p2 = 0 + -19 Reorder the terms: 19 + -19 + -2p + p2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -2p + p2 = 0 + -19 -2p + p2 = 0 + -19 Combine like terms: 0 + -19 = -19 -2p + p2 = -19 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = -19 + 1 Reorder the terms: 1 + -2p + p2 = -19 + 1 Combine like terms: -19 + 1 = -18 1 + -2p + p2 = -18 Factor a perfect square on the left side: (p + -1)(p + -1) = -18 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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