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Simplifying p2 + 5p + -19 = 0 Reorder the terms: -19 + 5p + p2 = 0 Solving -19 + 5p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 5p + 19 + p2 = 0 + 19 Reorder the terms: -19 + 19 + 5p + p2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 5p + p2 = 0 + 19 5p + p2 = 0 + 19 Combine like terms: 0 + 19 = 19 5p + p2 = 19 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = 19 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 19 + 6.25 Combine like terms: 19 + 6.25 = 25.25 6.25 + 5p + p2 = 25.25 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (p + 2.5) equal to 5.024937811 and -5.024937811.Subproblem 1
p + 2.5 = 5.024937811 Simplifying p + 2.5 = 5.024937811 Reorder the terms: 2.5 + p = 5.024937811 Solving 2.5 + p = 5.024937811 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 5.024937811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 5.024937811 + -2.5 p = 5.024937811 + -2.5 Combine like terms: 5.024937811 + -2.5 = 2.524937811 p = 2.524937811 Simplifying p = 2.524937811Subproblem 2
p + 2.5 = -5.024937811 Simplifying p + 2.5 = -5.024937811 Reorder the terms: 2.5 + p = -5.024937811 Solving 2.5 + p = -5.024937811 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -5.024937811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -5.024937811 + -2.5 p = -5.024937811 + -2.5 Combine like terms: -5.024937811 + -2.5 = -7.524937811 p = -7.524937811 Simplifying p = -7.524937811Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.524937811, -7.524937811}
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