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Simplifying 17p2 + 12p + -16 = 0 Reorder the terms: -16 + 12p + 17p2 = 0 Solving -16 + 12p + 17p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.9411764706 + 0.7058823529p + p2 = 0 Move the constant term to the right: Add '0.9411764706' to each side of the equation. -0.9411764706 + 0.7058823529p + 0.9411764706 + p2 = 0 + 0.9411764706 Reorder the terms: -0.9411764706 + 0.9411764706 + 0.7058823529p + p2 = 0 + 0.9411764706 Combine like terms: -0.9411764706 + 0.9411764706 = 0.0000000000 0.0000000000 + 0.7058823529p + p2 = 0 + 0.9411764706 0.7058823529p + p2 = 0 + 0.9411764706 Combine like terms: 0 + 0.9411764706 = 0.9411764706 0.7058823529p + p2 = 0.9411764706 The p term is 0.7058823529p. Take half its coefficient (0.3529411765). Square it (0.1245674741) and add it to both sides. Add '0.1245674741' to each side of the equation. 0.7058823529p + 0.1245674741 + p2 = 0.9411764706 + 0.1245674741 Reorder the terms: 0.1245674741 + 0.7058823529p + p2 = 0.9411764706 + 0.1245674741 Combine like terms: 0.9411764706 + 0.1245674741 = 1.0657439447 0.1245674741 + 0.7058823529p + p2 = 1.0657439447 Factor a perfect square on the left side: (p + 0.3529411765)(p + 0.3529411765) = 1.0657439447 Calculate the square root of the right side: 1.032348751 Break this problem into two subproblems by setting (p + 0.3529411765) equal to 1.032348751 and -1.032348751.Subproblem 1
p + 0.3529411765 = 1.032348751 Simplifying p + 0.3529411765 = 1.032348751 Reorder the terms: 0.3529411765 + p = 1.032348751 Solving 0.3529411765 + p = 1.032348751 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3529411765' to each side of the equation. 0.3529411765 + -0.3529411765 + p = 1.032348751 + -0.3529411765 Combine like terms: 0.3529411765 + -0.3529411765 = 0.0000000000 0.0000000000 + p = 1.032348751 + -0.3529411765 p = 1.032348751 + -0.3529411765 Combine like terms: 1.032348751 + -0.3529411765 = 0.6794075745 p = 0.6794075745 Simplifying p = 0.6794075745Subproblem 2
p + 0.3529411765 = -1.032348751 Simplifying p + 0.3529411765 = -1.032348751 Reorder the terms: 0.3529411765 + p = -1.032348751 Solving 0.3529411765 + p = -1.032348751 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3529411765' to each side of the equation. 0.3529411765 + -0.3529411765 + p = -1.032348751 + -0.3529411765 Combine like terms: 0.3529411765 + -0.3529411765 = 0.0000000000 0.0000000000 + p = -1.032348751 + -0.3529411765 p = -1.032348751 + -0.3529411765 Combine like terms: -1.032348751 + -0.3529411765 = -1.3852899275 p = -1.3852899275 Simplifying p = -1.3852899275Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.6794075745, -1.3852899275}
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