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Simplifying 10p2 + 11p + -17 = 0 Reorder the terms: -17 + 11p + 10p2 = 0 Solving -17 + 11p + 10p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.7 + 1.1p + p2 = 0 Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + 1.1p + 1.7 + p2 = 0 + 1.7 Reorder the terms: -1.7 + 1.7 + 1.1p + p2 = 0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + 1.1p + p2 = 0 + 1.7 1.1p + p2 = 0 + 1.7 Combine like terms: 0 + 1.7 = 1.7 1.1p + p2 = 1.7 The p term is 1.1p. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1p + 0.3025 + p2 = 1.7 + 0.3025 Reorder the terms: 0.3025 + 1.1p + p2 = 1.7 + 0.3025 Combine like terms: 1.7 + 0.3025 = 2.0025 0.3025 + 1.1p + p2 = 2.0025 Factor a perfect square on the left side: (p + 0.55)(p + 0.55) = 2.0025 Calculate the square root of the right side: 1.41509717 Break this problem into two subproblems by setting (p + 0.55) equal to 1.41509717 and -1.41509717.Subproblem 1
p + 0.55 = 1.41509717 Simplifying p + 0.55 = 1.41509717 Reorder the terms: 0.55 + p = 1.41509717 Solving 0.55 + p = 1.41509717 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + p = 1.41509717 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + p = 1.41509717 + -0.55 p = 1.41509717 + -0.55 Combine like terms: 1.41509717 + -0.55 = 0.86509717 p = 0.86509717 Simplifying p = 0.86509717Subproblem 2
p + 0.55 = -1.41509717 Simplifying p + 0.55 = -1.41509717 Reorder the terms: 0.55 + p = -1.41509717 Solving 0.55 + p = -1.41509717 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + p = -1.41509717 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + p = -1.41509717 + -0.55 p = -1.41509717 + -0.55 Combine like terms: -1.41509717 + -0.55 = -1.96509717 p = -1.96509717 Simplifying p = -1.96509717Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.86509717, -1.96509717}
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