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Simplifying 1800 = -2p2 + 70p + 822 Reorder the terms: 1800 = 822 + 70p + -2p2 Solving 1800 = 822 + 70p + -2p2 Solving for variable 'p'. Combine like terms: 1800 + -822 = 978 978 + -70p + 2p2 = 822 + 70p + -2p2 + -822 + -70p + 2p2 Reorder the terms: 978 + -70p + 2p2 = 822 + -822 + 70p + -70p + -2p2 + 2p2 Combine like terms: 822 + -822 = 0 978 + -70p + 2p2 = 0 + 70p + -70p + -2p2 + 2p2 978 + -70p + 2p2 = 70p + -70p + -2p2 + 2p2 Combine like terms: 70p + -70p = 0 978 + -70p + 2p2 = 0 + -2p2 + 2p2 978 + -70p + 2p2 = -2p2 + 2p2 Combine like terms: -2p2 + 2p2 = 0 978 + -70p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(489 + -35p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(489 + -35p + p2)' equal to zero and attempt to solve: Simplifying 489 + -35p + p2 = 0 Solving 489 + -35p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-489' to each side of the equation. 489 + -35p + -489 + p2 = 0 + -489 Reorder the terms: 489 + -489 + -35p + p2 = 0 + -489 Combine like terms: 489 + -489 = 0 0 + -35p + p2 = 0 + -489 -35p + p2 = 0 + -489 Combine like terms: 0 + -489 = -489 -35p + p2 = -489 The p term is -35p. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35p + 306.25 + p2 = -489 + 306.25 Reorder the terms: 306.25 + -35p + p2 = -489 + 306.25 Combine like terms: -489 + 306.25 = -182.75 306.25 + -35p + p2 = -182.75 Factor a perfect square on the left side: (p + -17.5)(p + -17.5) = -182.75 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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