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Simplifying 4p2 + -28p + 19 = 0 Reorder the terms: 19 + -28p + 4p2 = 0 Solving 19 + -28p + 4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.75 + -7p + p2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + -7p + -4.75 + p2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + -7p + p2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + -7p + p2 = 0 + -4.75 -7p + p2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 -7p + p2 = -4.75 The p term is -7p. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7p + 12.25 + p2 = -4.75 + 12.25 Reorder the terms: 12.25 + -7p + p2 = -4.75 + 12.25 Combine like terms: -4.75 + 12.25 = 7.5 12.25 + -7p + p2 = 7.5 Factor a perfect square on the left side: (p + -3.5)(p + -3.5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (p + -3.5) equal to 2.738612788 and -2.738612788.Subproblem 1
p + -3.5 = 2.738612788 Simplifying p + -3.5 = 2.738612788 Reorder the terms: -3.5 + p = 2.738612788 Solving -3.5 + p = 2.738612788 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = 2.738612788 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = 2.738612788 + 3.5 p = 2.738612788 + 3.5 Combine like terms: 2.738612788 + 3.5 = 6.238612788 p = 6.238612788 Simplifying p = 6.238612788Subproblem 2
p + -3.5 = -2.738612788 Simplifying p + -3.5 = -2.738612788 Reorder the terms: -3.5 + p = -2.738612788 Solving -3.5 + p = -2.738612788 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = -2.738612788 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = -2.738612788 + 3.5 p = -2.738612788 + 3.5 Combine like terms: -2.738612788 + 3.5 = 0.761387212 p = 0.761387212 Simplifying p = 0.761387212Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.238612788, 0.761387212}
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