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Simplifying 5(7p2 + -7p + 4) = 0 Reorder the terms: 5(4 + -7p + 7p2) = 0 (4 * 5 + -7p * 5 + 7p2 * 5) = 0 (20 + -35p + 35p2) = 0 Solving 20 + -35p + 35p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(4 + -7p + 7p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + -7p + 7p2)' equal to zero and attempt to solve: Simplifying 4 + -7p + 7p2 = 0 Solving 4 + -7p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + -1p + p2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -1p + -0.5714285714 + p2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -1p + p2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -1p + p2 = 0 + -0.5714285714 -1p + p2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -1p + p2 = -0.5714285714 The p term is -1p. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1p + 0.25 + p2 = -0.5714285714 + 0.25 Reorder the terms: 0.25 + -1p + p2 = -0.5714285714 + 0.25 Combine like terms: -0.5714285714 + 0.25 = -0.3214285714 0.25 + -1p + p2 = -0.3214285714 Factor a perfect square on the left side: (p + -0.5)(p + -0.5) = -0.3214285714 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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