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Simplifying 10p2 + 6p + -5 = 0 Reorder the terms: -5 + 6p + 10p2 = 0 Solving -5 + 6p + 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 + 0.6p + p2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.6p + 0.5 + p2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.6p + p2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.6p + p2 = 0 + 0.5 0.6p + p2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.6p + p2 = 0.5 The p term is 0.6p. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6p + 0.09 + p2 = 0.5 + 0.09 Reorder the terms: 0.09 + 0.6p + p2 = 0.5 + 0.09 Combine like terms: 0.5 + 0.09 = 0.59 0.09 + 0.6p + p2 = 0.59 Factor a perfect square on the left side: (p + 0.3)(p + 0.3) = 0.59 Calculate the square root of the right side: 0.768114575 Break this problem into two subproblems by setting (p + 0.3) equal to 0.768114575 and -0.768114575.Subproblem 1
p + 0.3 = 0.768114575 Simplifying p + 0.3 = 0.768114575 Reorder the terms: 0.3 + p = 0.768114575 Solving 0.3 + p = 0.768114575 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + p = 0.768114575 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + p = 0.768114575 + -0.3 p = 0.768114575 + -0.3 Combine like terms: 0.768114575 + -0.3 = 0.468114575 p = 0.468114575 Simplifying p = 0.468114575Subproblem 2
p + 0.3 = -0.768114575 Simplifying p + 0.3 = -0.768114575 Reorder the terms: 0.3 + p = -0.768114575 Solving 0.3 + p = -0.768114575 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + p = -0.768114575 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + p = -0.768114575 + -0.3 p = -0.768114575 + -0.3 Combine like terms: -0.768114575 + -0.3 = -1.068114575 p = -1.068114575 Simplifying p = -1.068114575Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.468114575, -1.068114575}
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