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Simplifying 6p2 + p = 13 Reorder the terms: p + 6p2 = 13 Solving p + 6p2 = 13 Solving for variable 'p'. Reorder the terms: -13 + p + 6p2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + p + 6p2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + 0.1666666667p + p2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + 0.1666666667p + 2.166666667 + p2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + 0.1666666667p + p2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + 0.1666666667p + p2 = 0 + 2.166666667 0.1666666667p + p2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 0.1666666667p + p2 = 2.166666667 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667p + 0.25 + p2 = 2.166666667 + 0.25 Reorder the terms: 0.25 + 0.1666666667p + p2 = 2.166666667 + 0.25 Combine like terms: 2.166666667 + 0.25 = 2.416666667 0.25 + 0.1666666667p + p2 = 2.416666667 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 2.416666667 Calculate the square root of the right side: 1.554563176 Break this problem into two subproblems by setting (p + 0.5) equal to 1.554563176 and -1.554563176.Subproblem 1
p + 0.5 = 1.554563176 Simplifying p + 0.5 = 1.554563176 Reorder the terms: 0.5 + p = 1.554563176 Solving 0.5 + p = 1.554563176 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 1.554563176 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 1.554563176 + -0.5 p = 1.554563176 + -0.5 Combine like terms: 1.554563176 + -0.5 = 1.054563176 p = 1.054563176 Simplifying p = 1.054563176Subproblem 2
p + 0.5 = -1.554563176 Simplifying p + 0.5 = -1.554563176 Reorder the terms: 0.5 + p = -1.554563176 Solving 0.5 + p = -1.554563176 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -1.554563176 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -1.554563176 + -0.5 p = -1.554563176 + -0.5 Combine like terms: -1.554563176 + -0.5 = -2.054563176 p = -2.054563176 Simplifying p = -2.054563176Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.054563176, -2.054563176}
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