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Simplifying 3p2 + 30 = 42p Reorder the terms: 30 + 3p2 = 42p Solving 30 + 3p2 = 42p Solving for variable 'p'. Reorder the terms: 30 + -42p + 3p2 = 42p + -42p Combine like terms: 42p + -42p = 0 30 + -42p + 3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -14p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -14p + p2)' equal to zero and attempt to solve: Simplifying 10 + -14p + p2 = 0 Solving 10 + -14p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -14p + -10 + p2 = 0 + -10 Reorder the terms: 10 + -10 + -14p + p2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -14p + p2 = 0 + -10 -14p + p2 = 0 + -10 Combine like terms: 0 + -10 = -10 -14p + p2 = -10 The p term is -14p. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14p + 49 + p2 = -10 + 49 Reorder the terms: 49 + -14p + p2 = -10 + 49 Combine like terms: -10 + 49 = 39 49 + -14p + p2 = 39 Factor a perfect square on the left side: (p + -7)(p + -7) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (p + -7) equal to 6.244997998 and -6.244997998.Subproblem 1
p + -7 = 6.244997998 Simplifying p + -7 = 6.244997998 Reorder the terms: -7 + p = 6.244997998 Solving -7 + p = 6.244997998 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = 6.244997998 + 7 Combine like terms: -7 + 7 = 0 0 + p = 6.244997998 + 7 p = 6.244997998 + 7 Combine like terms: 6.244997998 + 7 = 13.244997998 p = 13.244997998 Simplifying p = 13.244997998Subproblem 2
p + -7 = -6.244997998 Simplifying p + -7 = -6.244997998 Reorder the terms: -7 + p = -6.244997998 Solving -7 + p = -6.244997998 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = -6.244997998 + 7 Combine like terms: -7 + 7 = 0 0 + p = -6.244997998 + 7 p = -6.244997998 + 7 Combine like terms: -6.244997998 + 7 = 0.755002002 p = 0.755002002 Simplifying p = 0.755002002Solution
The solution to the problem is based on the solutions from the subproblems. p = {13.244997998, 0.755002002}Solution
p = {13.244997998, 0.755002002}
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