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Simplifying 3p2 + -30p + -11 = 6p Reorder the terms: -11 + -30p + 3p2 = 6p Solving -11 + -30p + 3p2 = 6p Solving for variable 'p'. Reorder the terms: -11 + -30p + -6p + 3p2 = 6p + -6p Combine like terms: -30p + -6p = -36p -11 + -36p + 3p2 = 6p + -6p Combine like terms: 6p + -6p = 0 -11 + -36p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + -12p + p2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + -12p + 3.666666667 + p2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + -12p + p2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + -12p + p2 = 0 + 3.666666667 -12p + p2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 -12p + p2 = 3.666666667 The p term is -12p. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12p + 36 + p2 = 3.666666667 + 36 Reorder the terms: 36 + -12p + p2 = 3.666666667 + 36 Combine like terms: 3.666666667 + 36 = 39.666666667 36 + -12p + p2 = 39.666666667 Factor a perfect square on the left side: (p + -6)(p + -6) = 39.666666667 Calculate the square root of the right side: 6.298147876 Break this problem into two subproblems by setting (p + -6) equal to 6.298147876 and -6.298147876.Subproblem 1
p + -6 = 6.298147876 Simplifying p + -6 = 6.298147876 Reorder the terms: -6 + p = 6.298147876 Solving -6 + p = 6.298147876 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = 6.298147876 + 6 Combine like terms: -6 + 6 = 0 0 + p = 6.298147876 + 6 p = 6.298147876 + 6 Combine like terms: 6.298147876 + 6 = 12.298147876 p = 12.298147876 Simplifying p = 12.298147876Subproblem 2
p + -6 = -6.298147876 Simplifying p + -6 = -6.298147876 Reorder the terms: -6 + p = -6.298147876 Solving -6 + p = -6.298147876 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = -6.298147876 + 6 Combine like terms: -6 + 6 = 0 0 + p = -6.298147876 + 6 p = -6.298147876 + 6 Combine like terms: -6.298147876 + 6 = -0.298147876 p = -0.298147876 Simplifying p = -0.298147876Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.298147876, -0.298147876}
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