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Simplifying 11(4p + 4) + -4p = -4p(7p + -7) Reorder the terms: 11(4 + 4p) + -4p = -4p(7p + -7) (4 * 11 + 4p * 11) + -4p = -4p(7p + -7) (44 + 44p) + -4p = -4p(7p + -7) Combine like terms: 44p + -4p = 40p 44 + 40p = -4p(7p + -7) Reorder the terms: 44 + 40p = -4p(-7 + 7p) 44 + 40p = (-7 * -4p + 7p * -4p) 44 + 40p = (28p + -28p2) Solving 44 + 40p = 28p + -28p2 Solving for variable 'p'. Combine like terms: 40p + -28p = 12p 44 + 12p + 28p2 = 28p + -28p2 + -28p + 28p2 Reorder the terms: 44 + 12p + 28p2 = 28p + -28p + -28p2 + 28p2 Combine like terms: 28p + -28p = 0 44 + 12p + 28p2 = 0 + -28p2 + 28p2 44 + 12p + 28p2 = -28p2 + 28p2 Combine like terms: -28p2 + 28p2 = 0 44 + 12p + 28p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(11 + 3p + 7p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + 3p + 7p2)' equal to zero and attempt to solve: Simplifying 11 + 3p + 7p2 = 0 Solving 11 + 3p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.571428571 + 0.4285714286p + p2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + 0.4285714286p + -1.571428571 + p2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + 0.4285714286p + p2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + 0.4285714286p + p2 = 0 + -1.571428571 0.4285714286p + p2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 0.4285714286p + p2 = -1.571428571 The p term is 0.4285714286p. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286p + 0.04591836735 + p2 = -1.571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286p + p2 = -1.571428571 + 0.04591836735 Combine like terms: -1.571428571 + 0.04591836735 = -1.52551020365 0.04591836735 + 0.4285714286p + p2 = -1.52551020365 Factor a perfect square on the left side: (p + 0.2142857143)(p + 0.2142857143) = -1.52551020365 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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