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Simplifying -21p2 + -24p = 12 Reorder the terms: -24p + -21p2 = 12 Solving -24p + -21p2 = 12 Solving for variable 'p'. Reorder the terms: -12 + -24p + -21p2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -24p + -21p2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(4 + 8p + 7p2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(4 + 8p + 7p2)' equal to zero and attempt to solve: Simplifying 4 + 8p + 7p2 = 0 Solving 4 + 8p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + 1.142857143p + p2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + 1.142857143p + -0.5714285714 + p2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + 1.142857143p + p2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + 1.142857143p + p2 = 0 + -0.5714285714 1.142857143p + p2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 1.142857143p + p2 = -0.5714285714 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 = -0.5714285714 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143p + p2 = -0.5714285714 + 0.3265306123 Combine like terms: -0.5714285714 + 0.3265306123 = -0.2448979591 0.3265306123 + 1.142857143p + p2 = -0.2448979591 Factor a perfect square on the left side: (p + 0.5714285715)(p + 0.5714285715) = -0.2448979591 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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