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Simplifying 524p2 + -14p + -3 = 0 Reorder the terms: -3 + -14p + 524p2 = 0 Solving -3 + -14p + 524p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 524 the coefficient of the squared term: Divide each side by '524'. -0.00572519084 + -0.02671755725p + p2 = 0 Move the constant term to the right: Add '0.00572519084' to each side of the equation. -0.00572519084 + -0.02671755725p + 0.00572519084 + p2 = 0 + 0.00572519084 Reorder the terms: -0.00572519084 + 0.00572519084 + -0.02671755725p + p2 = 0 + 0.00572519084 Combine like terms: -0.00572519084 + 0.00572519084 = 0.00000000000 0.00000000000 + -0.02671755725p + p2 = 0 + 0.00572519084 -0.02671755725p + p2 = 0 + 0.00572519084 Combine like terms: 0 + 0.00572519084 = 0.00572519084 -0.02671755725p + p2 = 0.00572519084 The p term is -0.02671755725p. Take half its coefficient (-0.01335877863). Square it (0.0001784569665) and add it to both sides. Add '0.0001784569665' to each side of the equation. -0.02671755725p + 0.0001784569665 + p2 = 0.00572519084 + 0.0001784569665 Reorder the terms: 0.0001784569665 + -0.02671755725p + p2 = 0.00572519084 + 0.0001784569665 Combine like terms: 0.00572519084 + 0.0001784569665 = 0.0059036478065 0.0001784569665 + -0.02671755725p + p2 = 0.0059036478065 Factor a perfect square on the left side: (p + -0.01335877863)(p + -0.01335877863) = 0.0059036478065 Calculate the square root of the right side: 0.076835199 Break this problem into two subproblems by setting (p + -0.01335877863) equal to 0.076835199 and -0.076835199.Subproblem 1
p + -0.01335877863 = 0.076835199 Simplifying p + -0.01335877863 = 0.076835199 Reorder the terms: -0.01335877863 + p = 0.076835199 Solving -0.01335877863 + p = 0.076835199 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.01335877863' to each side of the equation. -0.01335877863 + 0.01335877863 + p = 0.076835199 + 0.01335877863 Combine like terms: -0.01335877863 + 0.01335877863 = 0.00000000000 0.00000000000 + p = 0.076835199 + 0.01335877863 p = 0.076835199 + 0.01335877863 Combine like terms: 0.076835199 + 0.01335877863 = 0.09019397763 p = 0.09019397763 Simplifying p = 0.09019397763Subproblem 2
p + -0.01335877863 = -0.076835199 Simplifying p + -0.01335877863 = -0.076835199 Reorder the terms: -0.01335877863 + p = -0.076835199 Solving -0.01335877863 + p = -0.076835199 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.01335877863' to each side of the equation. -0.01335877863 + 0.01335877863 + p = -0.076835199 + 0.01335877863 Combine like terms: -0.01335877863 + 0.01335877863 = 0.00000000000 0.00000000000 + p = -0.076835199 + 0.01335877863 p = -0.076835199 + 0.01335877863 Combine like terms: -0.076835199 + 0.01335877863 = -0.06347642037 p = -0.06347642037 Simplifying p = -0.06347642037Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.09019397763, -0.06347642037}
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