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Simplifying 51p2 + -10p + -225 = 0 Reorder the terms: -225 + -10p + 51p2 = 0 Solving -225 + -10p + 51p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 51 the coefficient of the squared term: Divide each side by '51'. -4.411764706 + -0.1960784314p + p2 = 0 Move the constant term to the right: Add '4.411764706' to each side of the equation. -4.411764706 + -0.1960784314p + 4.411764706 + p2 = 0 + 4.411764706 Reorder the terms: -4.411764706 + 4.411764706 + -0.1960784314p + p2 = 0 + 4.411764706 Combine like terms: -4.411764706 + 4.411764706 = 0.000000000 0.000000000 + -0.1960784314p + p2 = 0 + 4.411764706 -0.1960784314p + p2 = 0 + 4.411764706 Combine like terms: 0 + 4.411764706 = 4.411764706 -0.1960784314p + p2 = 4.411764706 The p term is -0.1960784314p. Take half its coefficient (-0.0980392157). Square it (0.009611687815) and add it to both sides. Add '0.009611687815' to each side of the equation. -0.1960784314p + 0.009611687815 + p2 = 4.411764706 + 0.009611687815 Reorder the terms: 0.009611687815 + -0.1960784314p + p2 = 4.411764706 + 0.009611687815 Combine like terms: 4.411764706 + 0.009611687815 = 4.421376393815 0.009611687815 + -0.1960784314p + p2 = 4.421376393815 Factor a perfect square on the left side: (p + -0.0980392157)(p + -0.0980392157) = 4.421376393815 Calculate the square root of the right side: 2.102706921 Break this problem into two subproblems by setting (p + -0.0980392157) equal to 2.102706921 and -2.102706921.Subproblem 1
p + -0.0980392157 = 2.102706921 Simplifying p + -0.0980392157 = 2.102706921 Reorder the terms: -0.0980392157 + p = 2.102706921 Solving -0.0980392157 + p = 2.102706921 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.0980392157' to each side of the equation. -0.0980392157 + 0.0980392157 + p = 2.102706921 + 0.0980392157 Combine like terms: -0.0980392157 + 0.0980392157 = 0.0000000000 0.0000000000 + p = 2.102706921 + 0.0980392157 p = 2.102706921 + 0.0980392157 Combine like terms: 2.102706921 + 0.0980392157 = 2.2007461367 p = 2.2007461367 Simplifying p = 2.2007461367Subproblem 2
p + -0.0980392157 = -2.102706921 Simplifying p + -0.0980392157 = -2.102706921 Reorder the terms: -0.0980392157 + p = -2.102706921 Solving -0.0980392157 + p = -2.102706921 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.0980392157' to each side of the equation. -0.0980392157 + 0.0980392157 + p = -2.102706921 + 0.0980392157 Combine like terms: -0.0980392157 + 0.0980392157 = 0.0000000000 0.0000000000 + p = -2.102706921 + 0.0980392157 p = -2.102706921 + 0.0980392157 Combine like terms: -2.102706921 + 0.0980392157 = -2.0046677053 p = -2.0046677053 Simplifying p = -2.0046677053Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.2007461367, -2.0046677053}
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