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Simplifying 10p2 + -4p + -5 = 0 Reorder the terms: -5 + -4p + 10p2 = 0 Solving -5 + -4p + 10p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -0.4p + p2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.4p + 0.5 + p2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.4p + p2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.4p + p2 = 0 + 0.5 -0.4p + p2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.4p + p2 = 0.5 The p term is -0.4p. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4p + 0.04 + p2 = 0.5 + 0.04 Reorder the terms: 0.04 + -0.4p + p2 = 0.5 + 0.04 Combine like terms: 0.5 + 0.04 = 0.54 0.04 + -0.4p + p2 = 0.54 Factor a perfect square on the left side: (p + -0.2)(p + -0.2) = 0.54 Calculate the square root of the right side: 0.734846923 Break this problem into two subproblems by setting (p + -0.2) equal to 0.734846923 and -0.734846923.Subproblem 1
p + -0.2 = 0.734846923 Simplifying p + -0.2 = 0.734846923 Reorder the terms: -0.2 + p = 0.734846923 Solving -0.2 + p = 0.734846923 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + p = 0.734846923 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + p = 0.734846923 + 0.2 p = 0.734846923 + 0.2 Combine like terms: 0.734846923 + 0.2 = 0.934846923 p = 0.934846923 Simplifying p = 0.934846923Subproblem 2
p + -0.2 = -0.734846923 Simplifying p + -0.2 = -0.734846923 Reorder the terms: -0.2 + p = -0.734846923 Solving -0.2 + p = -0.734846923 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + p = -0.734846923 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + p = -0.734846923 + 0.2 p = -0.734846923 + 0.2 Combine like terms: -0.734846923 + 0.2 = -0.534846923 p = -0.534846923 Simplifying p = -0.534846923Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.934846923, -0.534846923}
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