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Simplifying 5.17p2 + -7.47p = 9 Reorder the terms: -7.47p + 5.17p2 = 9 Solving -7.47p + 5.17p2 = 9 Solving for variable 'p'. Reorder the terms: -9 + -7.47p + 5.17p2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -7.47p + 5.17p2 = 0 Begin completing the square. Divide all terms by 5.17 the coefficient of the squared term: Divide each side by '5.17'. -1.740812379 + -1.444874275p + p2 = 0 Move the constant term to the right: Add '1.740812379' to each side of the equation. -1.740812379 + -1.444874275p + 1.740812379 + p2 = 0 + 1.740812379 Reorder the terms: -1.740812379 + 1.740812379 + -1.444874275p + p2 = 0 + 1.740812379 Combine like terms: -1.740812379 + 1.740812379 = 0.000000000 0.000000000 + -1.444874275p + p2 = 0 + 1.740812379 -1.444874275p + p2 = 0 + 1.740812379 Combine like terms: 0 + 1.740812379 = 1.740812379 -1.444874275p + p2 = 1.740812379 The p term is -1.444874275p. Take half its coefficient (-0.7224371375). Square it (0.5219154176) and add it to both sides. Add '0.5219154176' to each side of the equation. -1.444874275p + 0.5219154176 + p2 = 1.740812379 + 0.5219154176 Reorder the terms: 0.5219154176 + -1.444874275p + p2 = 1.740812379 + 0.5219154176 Combine like terms: 1.740812379 + 0.5219154176 = 2.2627277966 0.5219154176 + -1.444874275p + p2 = 2.2627277966 Factor a perfect square on the left side: (p + -0.7224371375)(p + -0.7224371375) = 2.2627277966 Calculate the square root of the right side: 1.504236616 Break this problem into two subproblems by setting (p + -0.7224371375) equal to 1.504236616 and -1.504236616.Subproblem 1
p + -0.7224371375 = 1.504236616 Simplifying p + -0.7224371375 = 1.504236616 Reorder the terms: -0.7224371375 + p = 1.504236616 Solving -0.7224371375 + p = 1.504236616 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.7224371375' to each side of the equation. -0.7224371375 + 0.7224371375 + p = 1.504236616 + 0.7224371375 Combine like terms: -0.7224371375 + 0.7224371375 = 0.0000000000 0.0000000000 + p = 1.504236616 + 0.7224371375 p = 1.504236616 + 0.7224371375 Combine like terms: 1.504236616 + 0.7224371375 = 2.2266737535 p = 2.2266737535 Simplifying p = 2.2266737535Subproblem 2
p + -0.7224371375 = -1.504236616 Simplifying p + -0.7224371375 = -1.504236616 Reorder the terms: -0.7224371375 + p = -1.504236616 Solving -0.7224371375 + p = -1.504236616 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.7224371375' to each side of the equation. -0.7224371375 + 0.7224371375 + p = -1.504236616 + 0.7224371375 Combine like terms: -0.7224371375 + 0.7224371375 = 0.0000000000 0.0000000000 + p = -1.504236616 + 0.7224371375 p = -1.504236616 + 0.7224371375 Combine like terms: -1.504236616 + 0.7224371375 = -0.7817994785 p = -0.7817994785 Simplifying p = -0.7817994785Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.2266737535, -0.7817994785}
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