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Simplifying 10p2 + -24 = 3p Reorder the terms: -24 + 10p2 = 3p Solving -24 + 10p2 = 3p Solving for variable 'p'. Reorder the terms: -24 + -3p + 10p2 = 3p + -3p Combine like terms: 3p + -3p = 0 -24 + -3p + 10p2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.4 + -0.3p + p2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -0.3p + 2.4 + p2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -0.3p + p2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -0.3p + p2 = 0 + 2.4 -0.3p + p2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -0.3p + p2 = 2.4 The p term is -0.3p. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3p + 0.0225 + p2 = 2.4 + 0.0225 Reorder the terms: 0.0225 + -0.3p + p2 = 2.4 + 0.0225 Combine like terms: 2.4 + 0.0225 = 2.4225 0.0225 + -0.3p + p2 = 2.4225 Factor a perfect square on the left side: (p + -0.15)(p + -0.15) = 2.4225 Calculate the square root of the right side: 1.556438242 Break this problem into two subproblems by setting (p + -0.15) equal to 1.556438242 and -1.556438242.Subproblem 1
p + -0.15 = 1.556438242 Simplifying p + -0.15 = 1.556438242 Reorder the terms: -0.15 + p = 1.556438242 Solving -0.15 + p = 1.556438242 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + p = 1.556438242 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + p = 1.556438242 + 0.15 p = 1.556438242 + 0.15 Combine like terms: 1.556438242 + 0.15 = 1.706438242 p = 1.706438242 Simplifying p = 1.706438242Subproblem 2
p + -0.15 = -1.556438242 Simplifying p + -0.15 = -1.556438242 Reorder the terms: -0.15 + p = -1.556438242 Solving -0.15 + p = -1.556438242 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + p = -1.556438242 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + p = -1.556438242 + 0.15 p = -1.556438242 + 0.15 Combine like terms: -1.556438242 + 0.15 = -1.406438242 p = -1.406438242 Simplifying p = -1.406438242Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.706438242, -1.406438242}
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