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Simplifying 42p2 + -48p + 144 = 0 Reorder the terms: 144 + -48p + 42p2 = 0 Solving 144 + -48p + 42p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6'. 6(24 + -8p + 7p2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(24 + -8p + 7p2)' equal to zero and attempt to solve: Simplifying 24 + -8p + 7p2 = 0 Solving 24 + -8p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.428571429 + -1.142857143p + p2 = 0 Move the constant term to the right: Add '-3.428571429' to each side of the equation. 3.428571429 + -1.142857143p + -3.428571429 + p2 = 0 + -3.428571429 Reorder the terms: 3.428571429 + -3.428571429 + -1.142857143p + p2 = 0 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + -1.142857143p + p2 = 0 + -3.428571429 -1.142857143p + p2 = 0 + -3.428571429 Combine like terms: 0 + -3.428571429 = -3.428571429 -1.142857143p + p2 = -3.428571429 The p term is -1.142857143p. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143p + 0.3265306123 + p2 = -3.428571429 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143p + p2 = -3.428571429 + 0.3265306123 Combine like terms: -3.428571429 + 0.3265306123 = -3.1020408167 0.3265306123 + -1.142857143p + p2 = -3.1020408167 Factor a perfect square on the left side: (p + -0.5714285715)(p + -0.5714285715) = -3.1020408167 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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