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Simplifying 7p2 = 4 + -4p Solving 7p2 = 4 + -4p Solving for variable 'p'. Reorder the terms: -4 + 4p + 7p2 = 4 + -4p + -4 + 4p Reorder the terms: -4 + 4p + 7p2 = 4 + -4 + -4p + 4p Combine like terms: 4 + -4 = 0 -4 + 4p + 7p2 = 0 + -4p + 4p -4 + 4p + 7p2 = -4p + 4p Combine like terms: -4p + 4p = 0 -4 + 4p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 0.5714285714p + p2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.5714285714p + 0.5714285714 + p2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.5714285714p + p2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.5714285714p + p2 = 0 + 0.5714285714 0.5714285714p + p2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.5714285714p + p2 = 0.5714285714 The p term is 0.5714285714p. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714p + 0.08163265305 + p2 = 0.5714285714 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714p + p2 = 0.5714285714 + 0.08163265305 Combine like terms: 0.5714285714 + 0.08163265305 = 0.65306122445 0.08163265305 + 0.5714285714p + p2 = 0.65306122445 Factor a perfect square on the left side: (p + 0.2857142857)(p + 0.2857142857) = 0.65306122445 Calculate the square root of the right side: 0.808122036 Break this problem into two subproblems by setting (p + 0.2857142857) equal to 0.808122036 and -0.808122036.Subproblem 1
p + 0.2857142857 = 0.808122036 Simplifying p + 0.2857142857 = 0.808122036 Reorder the terms: 0.2857142857 + p = 0.808122036 Solving 0.2857142857 + p = 0.808122036 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + p = 0.808122036 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + p = 0.808122036 + -0.2857142857 p = 0.808122036 + -0.2857142857 Combine like terms: 0.808122036 + -0.2857142857 = 0.5224077503 p = 0.5224077503 Simplifying p = 0.5224077503Subproblem 2
p + 0.2857142857 = -0.808122036 Simplifying p + 0.2857142857 = -0.808122036 Reorder the terms: 0.2857142857 + p = -0.808122036 Solving 0.2857142857 + p = -0.808122036 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + p = -0.808122036 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + p = -0.808122036 + -0.2857142857 p = -0.808122036 + -0.2857142857 Combine like terms: -0.808122036 + -0.2857142857 = -1.0938363217 p = -1.0938363217 Simplifying p = -1.0938363217Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.5224077503, -1.0938363217}
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