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Simplifying p2 + 4p + -34 = 0 Reorder the terms: -34 + 4p + p2 = 0 Solving -34 + 4p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 4p + 34 + p2 = 0 + 34 Reorder the terms: -34 + 34 + 4p + p2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 4p + p2 = 0 + 34 4p + p2 = 0 + 34 Combine like terms: 0 + 34 = 34 4p + p2 = 34 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 34 + 4 Reorder the terms: 4 + 4p + p2 = 34 + 4 Combine like terms: 34 + 4 = 38 4 + 4p + p2 = 38 Factor a perfect square on the left side: (p + 2)(p + 2) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (p + 2) equal to 6.164414003 and -6.164414003.Subproblem 1
p + 2 = 6.164414003 Simplifying p + 2 = 6.164414003 Reorder the terms: 2 + p = 6.164414003 Solving 2 + p = 6.164414003 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 6.164414003 + -2 Combine like terms: 2 + -2 = 0 0 + p = 6.164414003 + -2 p = 6.164414003 + -2 Combine like terms: 6.164414003 + -2 = 4.164414003 p = 4.164414003 Simplifying p = 4.164414003Subproblem 2
p + 2 = -6.164414003 Simplifying p + 2 = -6.164414003 Reorder the terms: 2 + p = -6.164414003 Solving 2 + p = -6.164414003 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -6.164414003 + -2 Combine like terms: 2 + -2 = 0 0 + p = -6.164414003 + -2 p = -6.164414003 + -2 Combine like terms: -6.164414003 + -2 = -8.164414003 p = -8.164414003 Simplifying p = -8.164414003Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.164414003, -8.164414003}
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