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Simplifying 56 + 5p + -1p2 = 0 Solving 56 + 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'. -56 + -5p + p2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + -5p + 56 + p2 = 0 + 56 Reorder the terms: -56 + 56 + -5p + p2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -5p + p2 = 0 + 56 -5p + p2 = 0 + 56 Combine like terms: 0 + 56 = 56 -5p + p2 = 56 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 = 56 + 6.25 Reorder the terms: 6.25 + -5p + p2 = 56 + 6.25 Combine like terms: 56 + 6.25 = 62.25 6.25 + -5p + p2 = 62.25 Factor a perfect square on the left side: (p + -2.5)(p + -2.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (p + -2.5) equal to 7.889866919 and -7.889866919.Subproblem 1
p + -2.5 = 7.889866919 Simplifying p + -2.5 = 7.889866919 Reorder the terms: -2.5 + p = 7.889866919 Solving -2.5 + p = 7.889866919 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 = 7.889866919 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = 7.889866919 + 2.5 p = 7.889866919 + 2.5 Combine like terms: 7.889866919 + 2.5 = 10.389866919 p = 10.389866919 Simplifying p = 10.389866919Subproblem 2
p + -2.5 = -7.889866919 Simplifying p + -2.5 = -7.889866919 Reorder the terms: -2.5 + p = -7.889866919 Solving -2.5 + p = -7.889866919 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 = -7.889866919 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = -7.889866919 + 2.5 p = -7.889866919 + 2.5 Combine like terms: -7.889866919 + 2.5 = -5.389866919 p = -5.389866919 Simplifying p = -5.389866919Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.389866919, -5.389866919}
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