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Simplifying 110p2 + -9 = 9p Reorder the terms: -9 + 110p2 = 9p Solving -9 + 110p2 = 9p Solving for variable 'p'. Reorder the terms: -9 + -9p + 110p2 = 9p + -9p Combine like terms: 9p + -9p = 0 -9 + -9p + 110p2 = 0 Begin completing the square. Divide all terms by 110 the coefficient of the squared term: Divide each side by '110'. -0.08181818182 + -0.08181818182p + p2 = 0 Move the constant term to the right: Add '0.08181818182' to each side of the equation. -0.08181818182 + -0.08181818182p + 0.08181818182 + p2 = 0 + 0.08181818182 Reorder the terms: -0.08181818182 + 0.08181818182 + -0.08181818182p + p2 = 0 + 0.08181818182 Combine like terms: -0.08181818182 + 0.08181818182 = 0.00000000000 0.00000000000 + -0.08181818182p + p2 = 0 + 0.08181818182 -0.08181818182p + p2 = 0 + 0.08181818182 Combine like terms: 0 + 0.08181818182 = 0.08181818182 -0.08181818182p + p2 = 0.08181818182 The p term is -0.08181818182p. Take half its coefficient (-0.04090909091). Square it (0.001673553719) and add it to both sides. Add '0.001673553719' to each side of the equation. -0.08181818182p + 0.001673553719 + p2 = 0.08181818182 + 0.001673553719 Reorder the terms: 0.001673553719 + -0.08181818182p + p2 = 0.08181818182 + 0.001673553719 Combine like terms: 0.08181818182 + 0.001673553719 = 0.083491735539 0.001673553719 + -0.08181818182p + p2 = 0.083491735539 Factor a perfect square on the left side: (p + -0.04090909091)(p + -0.04090909091) = 0.083491735539 Calculate the square root of the right side: 0.288949365 Break this problem into two subproblems by setting (p + -0.04090909091) equal to 0.288949365 and -0.288949365.Subproblem 1
p + -0.04090909091 = 0.288949365 Simplifying p + -0.04090909091 = 0.288949365 Reorder the terms: -0.04090909091 + p = 0.288949365 Solving -0.04090909091 + p = 0.288949365 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.04090909091' to each side of the equation. -0.04090909091 + 0.04090909091 + p = 0.288949365 + 0.04090909091 Combine like terms: -0.04090909091 + 0.04090909091 = 0.00000000000 0.00000000000 + p = 0.288949365 + 0.04090909091 p = 0.288949365 + 0.04090909091 Combine like terms: 0.288949365 + 0.04090909091 = 0.32985845591 p = 0.32985845591 Simplifying p = 0.32985845591Subproblem 2
p + -0.04090909091 = -0.288949365 Simplifying p + -0.04090909091 = -0.288949365 Reorder the terms: -0.04090909091 + p = -0.288949365 Solving -0.04090909091 + p = -0.288949365 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.04090909091' to each side of the equation. -0.04090909091 + 0.04090909091 + p = -0.288949365 + 0.04090909091 Combine like terms: -0.04090909091 + 0.04090909091 = 0.00000000000 0.00000000000 + p = -0.288949365 + 0.04090909091 p = -0.288949365 + 0.04090909091 Combine like terms: -0.288949365 + 0.04090909091 = -0.24804027409 p = -0.24804027409 Simplifying p = -0.24804027409Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.32985845591, -0.24804027409}
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