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Simplifying 650 + -5p + -1p2 = 0 Solving 650 + -5p + -1p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -650 + 5p + p2 = 0 Move the constant term to the right: Add '650' to each side of the equation. -650 + 5p + 650 + p2 = 0 + 650 Reorder the terms: -650 + 650 + 5p + p2 = 0 + 650 Combine like terms: -650 + 650 = 0 0 + 5p + p2 = 0 + 650 5p + p2 = 0 + 650 Combine like terms: 0 + 650 = 650 5p + p2 = 650 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 = 650 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 650 + 6.25 Combine like terms: 650 + 6.25 = 656.25 6.25 + 5p + p2 = 656.25 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 656.25 Calculate the square root of the right side: 25.617376915 Break this problem into two subproblems by setting (p + 2.5) equal to 25.617376915 and -25.617376915.Subproblem 1
p + 2.5 = 25.617376915 Simplifying p + 2.5 = 25.617376915 Reorder the terms: 2.5 + p = 25.617376915 Solving 2.5 + p = 25.617376915 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 = 25.617376915 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 25.617376915 + -2.5 p = 25.617376915 + -2.5 Combine like terms: 25.617376915 + -2.5 = 23.117376915 p = 23.117376915 Simplifying p = 23.117376915Subproblem 2
p + 2.5 = -25.617376915 Simplifying p + 2.5 = -25.617376915 Reorder the terms: 2.5 + p = -25.617376915 Solving 2.5 + p = -25.617376915 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 = -25.617376915 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -25.617376915 + -2.5 p = -25.617376915 + -2.5 Combine like terms: -25.617376915 + -2.5 = -28.117376915 p = -28.117376915 Simplifying p = -28.117376915Solution
The solution to the problem is based on the solutions from the subproblems. p = {23.117376915, -28.117376915}
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