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Simplifying 8p2 + -116p + 360 = -29 Reorder the terms: 360 + -116p + 8p2 = -29 Solving 360 + -116p + 8p2 = -29 Solving for variable 'p'. Reorder the terms: 360 + 29 + -116p + 8p2 = -29 + 29 Combine like terms: 360 + 29 = 389 389 + -116p + 8p2 = -29 + 29 Combine like terms: -29 + 29 = 0 389 + -116p + 8p2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 48.625 + -14.5p + p2 = 0 Move the constant term to the right: Add '-48.625' to each side of the equation. 48.625 + -14.5p + -48.625 + p2 = 0 + -48.625 Reorder the terms: 48.625 + -48.625 + -14.5p + p2 = 0 + -48.625 Combine like terms: 48.625 + -48.625 = 0.000 0.000 + -14.5p + p2 = 0 + -48.625 -14.5p + p2 = 0 + -48.625 Combine like terms: 0 + -48.625 = -48.625 -14.5p + p2 = -48.625 The p term is -14.5p. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5p + 52.5625 + p2 = -48.625 + 52.5625 Reorder the terms: 52.5625 + -14.5p + p2 = -48.625 + 52.5625 Combine like terms: -48.625 + 52.5625 = 3.9375 52.5625 + -14.5p + p2 = 3.9375 Factor a perfect square on the left side: (p + -7.25)(p + -7.25) = 3.9375 Calculate the square root of the right side: 1.984313483 Break this problem into two subproblems by setting (p + -7.25) equal to 1.984313483 and -1.984313483.Subproblem 1
p + -7.25 = 1.984313483 Simplifying p + -7.25 = 1.984313483 Reorder the terms: -7.25 + p = 1.984313483 Solving -7.25 + p = 1.984313483 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + p = 1.984313483 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + p = 1.984313483 + 7.25 p = 1.984313483 + 7.25 Combine like terms: 1.984313483 + 7.25 = 9.234313483 p = 9.234313483 Simplifying p = 9.234313483Subproblem 2
p + -7.25 = -1.984313483 Simplifying p + -7.25 = -1.984313483 Reorder the terms: -7.25 + p = -1.984313483 Solving -7.25 + p = -1.984313483 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + p = -1.984313483 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + p = -1.984313483 + 7.25 p = -1.984313483 + 7.25 Combine like terms: -1.984313483 + 7.25 = 5.265686517 p = 5.265686517 Simplifying p = 5.265686517Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.234313483, 5.265686517}
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