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Simplifying 7 = 6p + 6p2 Solving 7 = 6p + 6p2 Solving for variable 'p'. Reorder the terms: 7 + -6p + -6p2 = 6p + -6p + 6p2 + -6p2 Combine like terms: 6p + -6p = 0 7 + -6p + -6p2 = 0 + 6p2 + -6p2 7 + -6p + -6p2 = 6p2 + -6p2 Combine like terms: 6p2 + -6p2 = 0 7 + -6p + -6p2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.166666667 + p + p2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + p + 1.166666667 + p2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + p + p2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + p + p2 = 0 + 1.166666667 p + p2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 p + p2 = 1.166666667 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. + 0.25 + p2 = 1.166666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + p2 = 1.166666667 + 0.25 Combine like terms: 1.166666667 + 0.25 = 1.416666667 1.25 + p2 = 1.416666667 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 1.416666667 Calculate the square root of the right side: 1.190238072 Break this problem into two subproblems by setting (p + 0.5) equal to 1.190238072 and -1.190238072.Subproblem 1
p + 0.5 = 1.190238072 Simplifying p + 0.5 = 1.190238072 Reorder the terms: 0.5 + p = 1.190238072 Solving 0.5 + p = 1.190238072 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 = 1.190238072 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 1.190238072 + -0.5 p = 1.190238072 + -0.5 Combine like terms: 1.190238072 + -0.5 = 0.690238072 p = 0.690238072 Simplifying p = 0.690238072Subproblem 2
p + 0.5 = -1.190238072 Simplifying p + 0.5 = -1.190238072 Reorder the terms: 0.5 + p = -1.190238072 Solving 0.5 + p = -1.190238072 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 = -1.190238072 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -1.190238072 + -0.5 p = -1.190238072 + -0.5 Combine like terms: -1.190238072 + -0.5 = -1.690238072 p = -1.690238072 Simplifying p = -1.690238072Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.690238072, -1.690238072}
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