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Simplifying p2 + 7p + 7 = 0 Reorder the terms: 7 + 7p + p2 = 0 Solving 7 + 7p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 7p + -7 + p2 = 0 + -7 Reorder the terms: 7 + -7 + 7p + p2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7p + p2 = 0 + -7 7p + p2 = 0 + -7 Combine like terms: 0 + -7 = -7 7p + p2 = -7 The p term is 7p. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7p + 12.25 + p2 = -7 + 12.25 Reorder the terms: 12.25 + 7p + p2 = -7 + 12.25 Combine like terms: -7 + 12.25 = 5.25 12.25 + 7p + p2 = 5.25 Factor a perfect square on the left side: (p + 3.5)(p + 3.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (p + 3.5) equal to 2.291287847 and -2.291287847.Subproblem 1
p + 3.5 = 2.291287847 Simplifying p + 3.5 = 2.291287847 Reorder the terms: 3.5 + p = 2.291287847 Solving 3.5 + p = 2.291287847 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + p = 2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = 2.291287847 + -3.5 p = 2.291287847 + -3.5 Combine like terms: 2.291287847 + -3.5 = -1.208712153 p = -1.208712153 Simplifying p = -1.208712153Subproblem 2
p + 3.5 = -2.291287847 Simplifying p + 3.5 = -2.291287847 Reorder the terms: 3.5 + p = -2.291287847 Solving 3.5 + p = -2.291287847 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + p = -2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = -2.291287847 + -3.5 p = -2.291287847 + -3.5 Combine like terms: -2.291287847 + -3.5 = -5.791287847 p = -5.791287847 Simplifying p = -5.791287847Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.208712153, -5.791287847}
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