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Simplifying 12p2 + -21p + 27 = 0 Reorder the terms: 27 + -21p + 12p2 = 0 Solving 27 + -21p + 12p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -7p + 4p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -7p + 4p2)' equal to zero and attempt to solve: Simplifying 9 + -7p + 4p2 = 0 Solving 9 + -7p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -1.75p + p2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -1.75p + -2.25 + p2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -1.75p + p2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -1.75p + p2 = 0 + -2.25 -1.75p + p2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -1.75p + p2 = -2.25 The p term is -1.75p. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75p + 0.765625 + p2 = -2.25 + 0.765625 Reorder the terms: 0.765625 + -1.75p + p2 = -2.25 + 0.765625 Combine like terms: -2.25 + 0.765625 = -1.484375 0.765625 + -1.75p + p2 = -1.484375 Factor a perfect square on the left side: (p + -0.875)(p + -0.875) = -1.484375 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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