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Simplifying -2(p + -5) * 7p = -5 Reorder the terms: -2(-5 + p) * 7p = -5 Reorder the terms for easier multiplication: -2 * 7p(-5 + p) = -5 Multiply -2 * 7 -14p(-5 + p) = -5 (-5 * -14p + p * -14p) = -5 (70p + -14p2) = -5 Solving 70p + -14p2 = -5 Solving for variable 'p'. Reorder the terms: 5 + 70p + -14p2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 70p + -14p2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.3571428571 + -5p + p2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + -5p + 0.3571428571 + p2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + -5p + p2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + -5p + p2 = 0 + 0.3571428571 -5p + p2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 -5p + p2 = 0.3571428571 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 = 0.3571428571 + 6.25 Reorder the terms: 6.25 + -5p + p2 = 0.3571428571 + 6.25 Combine like terms: 0.3571428571 + 6.25 = 6.6071428571 6.25 + -5p + p2 = 6.6071428571 Factor a perfect square on the left side: (p + -2.5)(p + -2.5) = 6.6071428571 Calculate the square root of the right side: 2.570436316 Break this problem into two subproblems by setting (p + -2.5) equal to 2.570436316 and -2.570436316.Subproblem 1
p + -2.5 = 2.570436316 Simplifying p + -2.5 = 2.570436316 Reorder the terms: -2.5 + p = 2.570436316 Solving -2.5 + p = 2.570436316 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 = 2.570436316 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = 2.570436316 + 2.5 p = 2.570436316 + 2.5 Combine like terms: 2.570436316 + 2.5 = 5.070436316 p = 5.070436316 Simplifying p = 5.070436316Subproblem 2
p + -2.5 = -2.570436316 Simplifying p + -2.5 = -2.570436316 Reorder the terms: -2.5 + p = -2.570436316 Solving -2.5 + p = -2.570436316 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 = -2.570436316 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = -2.570436316 + 2.5 p = -2.570436316 + 2.5 Combine like terms: -2.570436316 + 2.5 = -0.070436316 p = -0.070436316 Simplifying p = -0.070436316Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.070436316, -0.070436316}
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