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Simplifying 10p2 + -3p + -97 = 3p Reorder the terms: -97 + -3p + 10p2 = 3p Solving -97 + -3p + 10p2 = 3p Solving for variable 'p'. Reorder the terms: -97 + -3p + -3p + 10p2 = 3p + -3p Combine like terms: -3p + -3p = -6p -97 + -6p + 10p2 = 3p + -3p Combine like terms: 3p + -3p = 0 -97 + -6p + 10p2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -9.7 + -0.6p + p2 = 0 Move the constant term to the right: Add '9.7' to each side of the equation. -9.7 + -0.6p + 9.7 + p2 = 0 + 9.7 Reorder the terms: -9.7 + 9.7 + -0.6p + p2 = 0 + 9.7 Combine like terms: -9.7 + 9.7 = 0.0 0.0 + -0.6p + p2 = 0 + 9.7 -0.6p + p2 = 0 + 9.7 Combine like terms: 0 + 9.7 = 9.7 -0.6p + p2 = 9.7 The p term is -0.6p. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6p + 0.09 + p2 = 9.7 + 0.09 Reorder the terms: 0.09 + -0.6p + p2 = 9.7 + 0.09 Combine like terms: 9.7 + 0.09 = 9.79 0.09 + -0.6p + p2 = 9.79 Factor a perfect square on the left side: (p + -0.3)(p + -0.3) = 9.79 Calculate the square root of the right side: 3.128897569 Break this problem into two subproblems by setting (p + -0.3) equal to 3.128897569 and -3.128897569.Subproblem 1
p + -0.3 = 3.128897569 Simplifying p + -0.3 = 3.128897569 Reorder the terms: -0.3 + p = 3.128897569 Solving -0.3 + p = 3.128897569 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + p = 3.128897569 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + p = 3.128897569 + 0.3 p = 3.128897569 + 0.3 Combine like terms: 3.128897569 + 0.3 = 3.428897569 p = 3.428897569 Simplifying p = 3.428897569Subproblem 2
p + -0.3 = -3.128897569 Simplifying p + -0.3 = -3.128897569 Reorder the terms: -0.3 + p = -3.128897569 Solving -0.3 + p = -3.128897569 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + p = -3.128897569 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + p = -3.128897569 + 0.3 p = -3.128897569 + 0.3 Combine like terms: -3.128897569 + 0.3 = -2.828897569 p = -2.828897569 Simplifying p = -2.828897569Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.428897569, -2.828897569}
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