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Simplifying p2 + 6p + -100 = 0 Reorder the terms: -100 + 6p + p2 = 0 Solving -100 + 6p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 6p + 100 + p2 = 0 + 100 Reorder the terms: -100 + 100 + 6p + p2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 6p + p2 = 0 + 100 6p + p2 = 0 + 100 Combine like terms: 0 + 100 = 100 6p + p2 = 100 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 100 + 9 Reorder the terms: 9 + 6p + p2 = 100 + 9 Combine like terms: 100 + 9 = 109 9 + 6p + p2 = 109 Factor a perfect square on the left side: (p + 3)(p + 3) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (p + 3) equal to 10.440306509 and -10.440306509.Subproblem 1
p + 3 = 10.440306509 Simplifying p + 3 = 10.440306509 Reorder the terms: 3 + p = 10.440306509 Solving 3 + p = 10.440306509 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 10.440306509 + -3 Combine like terms: 3 + -3 = 0 0 + p = 10.440306509 + -3 p = 10.440306509 + -3 Combine like terms: 10.440306509 + -3 = 7.440306509 p = 7.440306509 Simplifying p = 7.440306509Subproblem 2
p + 3 = -10.440306509 Simplifying p + 3 = -10.440306509 Reorder the terms: 3 + p = -10.440306509 Solving 3 + p = -10.440306509 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -10.440306509 + -3 Combine like terms: 3 + -3 = 0 0 + p = -10.440306509 + -3 p = -10.440306509 + -3 Combine like terms: -10.440306509 + -3 = -13.440306509 p = -13.440306509 Simplifying p = -13.440306509Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.440306509, -13.440306509}
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