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Simplifying 16p2 + 79p + -3 = 0 Reorder the terms: -3 + 79p + 16p2 = 0 Solving -3 + 79p + 16p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + 4.9375p + p2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 4.9375p + 0.1875 + p2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 4.9375p + p2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 4.9375p + p2 = 0 + 0.1875 4.9375p + p2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 4.9375p + p2 = 0.1875 The p term is 4.9375p. Take half its coefficient (2.46875). Square it (6.094726563) and add it to both sides. Add '6.094726563' to each side of the equation. 4.9375p + 6.094726563 + p2 = 0.1875 + 6.094726563 Reorder the terms: 6.094726563 + 4.9375p + p2 = 0.1875 + 6.094726563 Combine like terms: 0.1875 + 6.094726563 = 6.282226563 6.094726563 + 4.9375p + p2 = 6.282226563 Factor a perfect square on the left side: (p + 2.46875)(p + 2.46875) = 6.282226563 Calculate the square root of the right side: 2.506437026 Break this problem into two subproblems by setting (p + 2.46875) equal to 2.506437026 and -2.506437026.Subproblem 1
p + 2.46875 = 2.506437026 Simplifying p + 2.46875 = 2.506437026 Reorder the terms: 2.46875 + p = 2.506437026 Solving 2.46875 + p = 2.506437026 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.46875' to each side of the equation. 2.46875 + -2.46875 + p = 2.506437026 + -2.46875 Combine like terms: 2.46875 + -2.46875 = 0.00000 0.00000 + p = 2.506437026 + -2.46875 p = 2.506437026 + -2.46875 Combine like terms: 2.506437026 + -2.46875 = 0.037687026 p = 0.037687026 Simplifying p = 0.037687026Subproblem 2
p + 2.46875 = -2.506437026 Simplifying p + 2.46875 = -2.506437026 Reorder the terms: 2.46875 + p = -2.506437026 Solving 2.46875 + p = -2.506437026 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.46875' to each side of the equation. 2.46875 + -2.46875 + p = -2.506437026 + -2.46875 Combine like terms: 2.46875 + -2.46875 = 0.00000 0.00000 + p = -2.506437026 + -2.46875 p = -2.506437026 + -2.46875 Combine like terms: -2.506437026 + -2.46875 = -4.975187026 p = -4.975187026 Simplifying p = -4.975187026Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.037687026, -4.975187026}
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