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Simplifying 5p2 + -13p + 7 = 0 Reorder the terms: 7 + -13p + 5p2 = 0 Solving 7 + -13p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -2.6p + p2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -2.6p + -1.4 + p2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -2.6p + p2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -2.6p + p2 = 0 + -1.4 -2.6p + p2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -2.6p + p2 = -1.4 The p term is -2.6p. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6p + 1.69 + p2 = -1.4 + 1.69 Reorder the terms: 1.69 + -2.6p + p2 = -1.4 + 1.69 Combine like terms: -1.4 + 1.69 = 0.29 1.69 + -2.6p + p2 = 0.29 Factor a perfect square on the left side: (p + -1.3)(p + -1.3) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (p + -1.3) equal to 0.538516481 and -0.538516481.Subproblem 1
p + -1.3 = 0.538516481 Simplifying p + -1.3 = 0.538516481 Reorder the terms: -1.3 + p = 0.538516481 Solving -1.3 + p = 0.538516481 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + p = 0.538516481 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + p = 0.538516481 + 1.3 p = 0.538516481 + 1.3 Combine like terms: 0.538516481 + 1.3 = 1.838516481 p = 1.838516481 Simplifying p = 1.838516481Subproblem 2
p + -1.3 = -0.538516481 Simplifying p + -1.3 = -0.538516481 Reorder the terms: -1.3 + p = -0.538516481 Solving -1.3 + p = -0.538516481 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + p = -0.538516481 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + p = -0.538516481 + 1.3 p = -0.538516481 + 1.3 Combine like terms: -0.538516481 + 1.3 = 0.761483519 p = 0.761483519 Simplifying p = 0.761483519Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.838516481, 0.761483519}
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