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Simplifying 9p2 + -50p + -22 = 0 Reorder the terms: -22 + -50p + 9p2 = 0 Solving -22 + -50p + 9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.444444444 + -5.555555556p + p2 = 0 Move the constant term to the right: Add '2.444444444' to each side of the equation. -2.444444444 + -5.555555556p + 2.444444444 + p2 = 0 + 2.444444444 Reorder the terms: -2.444444444 + 2.444444444 + -5.555555556p + p2 = 0 + 2.444444444 Combine like terms: -2.444444444 + 2.444444444 = 0.000000000 0.000000000 + -5.555555556p + p2 = 0 + 2.444444444 -5.555555556p + p2 = 0 + 2.444444444 Combine like terms: 0 + 2.444444444 = 2.444444444 -5.555555556p + p2 = 2.444444444 The p term is -5.555555556p. Take half its coefficient (-2.777777778). Square it (7.716049384) and add it to both sides. Add '7.716049384' to each side of the equation. -5.555555556p + 7.716049384 + p2 = 2.444444444 + 7.716049384 Reorder the terms: 7.716049384 + -5.555555556p + p2 = 2.444444444 + 7.716049384 Combine like terms: 2.444444444 + 7.716049384 = 10.160493828 7.716049384 + -5.555555556p + p2 = 10.160493828 Factor a perfect square on the left side: (p + -2.777777778)(p + -2.777777778) = 10.160493828 Calculate the square root of the right side: 3.187552953 Break this problem into two subproblems by setting (p + -2.777777778) equal to 3.187552953 and -3.187552953.Subproblem 1
p + -2.777777778 = 3.187552953 Simplifying p + -2.777777778 = 3.187552953 Reorder the terms: -2.777777778 + p = 3.187552953 Solving -2.777777778 + p = 3.187552953 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + p = 3.187552953 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + p = 3.187552953 + 2.777777778 p = 3.187552953 + 2.777777778 Combine like terms: 3.187552953 + 2.777777778 = 5.965330731 p = 5.965330731 Simplifying p = 5.965330731Subproblem 2
p + -2.777777778 = -3.187552953 Simplifying p + -2.777777778 = -3.187552953 Reorder the terms: -2.777777778 + p = -3.187552953 Solving -2.777777778 + p = -3.187552953 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + p = -3.187552953 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + p = -3.187552953 + 2.777777778 p = -3.187552953 + 2.777777778 Combine like terms: -3.187552953 + 2.777777778 = -0.409775175 p = -0.409775175 Simplifying p = -0.409775175Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.965330731, -0.409775175}
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