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Simplifying -4p(3p + 4) + -11 = 3(4p + 7) Reorder the terms: -4p(4 + 3p) + -11 = 3(4p + 7) (4 * -4p + 3p * -4p) + -11 = 3(4p + 7) (-16p + -12p2) + -11 = 3(4p + 7) Reorder the terms: -11 + -16p + -12p2 = 3(4p + 7) Reorder the terms: -11 + -16p + -12p2 = 3(7 + 4p) -11 + -16p + -12p2 = (7 * 3 + 4p * 3) -11 + -16p + -12p2 = (21 + 12p) Solving -11 + -16p + -12p2 = 21 + 12p Solving for variable 'p'. Reorder the terms: -11 + -21 + -16p + -12p + -12p2 = 21 + 12p + -21 + -12p Combine like terms: -11 + -21 = -32 -32 + -16p + -12p + -12p2 = 21 + 12p + -21 + -12p Combine like terms: -16p + -12p = -28p -32 + -28p + -12p2 = 21 + 12p + -21 + -12p Reorder the terms: -32 + -28p + -12p2 = 21 + -21 + 12p + -12p Combine like terms: 21 + -21 = 0 -32 + -28p + -12p2 = 0 + 12p + -12p -32 + -28p + -12p2 = 12p + -12p Combine like terms: 12p + -12p = 0 -32 + -28p + -12p2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(8 + 7p + 3p2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(8 + 7p + 3p2)' equal to zero and attempt to solve: Simplifying 8 + 7p + 3p2 = 0 Solving 8 + 7p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 2.333333333p + p2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 2.333333333p + -2.666666667 + p2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 2.333333333p + p2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 2.333333333p + p2 = 0 + -2.666666667 2.333333333p + p2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 2.333333333p + p2 = -2.666666667 The p term is 2.333333333p. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333p + 1.361111112 + p2 = -2.666666667 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333p + p2 = -2.666666667 + 1.361111112 Combine like terms: -2.666666667 + 1.361111112 = -1.305555555 1.361111112 + 2.333333333p + p2 = -1.305555555 Factor a perfect square on the left side: (p + 1.166666667)(p + 1.166666667) = -1.305555555 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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