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Simplifying 6p2 + 192p = -172 Reorder the terms: 192p + 6p2 = -172 Solving 192p + 6p2 = -172 Solving for variable 'p'. Reorder the terms: 172 + 192p + 6p2 = -172 + 172 Combine like terms: -172 + 172 = 0 172 + 192p + 6p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(86 + 96p + 3p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(86 + 96p + 3p2)' equal to zero and attempt to solve: Simplifying 86 + 96p + 3p2 = 0 Solving 86 + 96p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 28.66666667 + 32p + p2 = 0 Move the constant term to the right: Add '-28.66666667' to each side of the equation. 28.66666667 + 32p + -28.66666667 + p2 = 0 + -28.66666667 Reorder the terms: 28.66666667 + -28.66666667 + 32p + p2 = 0 + -28.66666667 Combine like terms: 28.66666667 + -28.66666667 = 0.00000000 0.00000000 + 32p + p2 = 0 + -28.66666667 32p + p2 = 0 + -28.66666667 Combine like terms: 0 + -28.66666667 = -28.66666667 32p + p2 = -28.66666667 The p term is 32p. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32p + 256 + p2 = -28.66666667 + 256 Reorder the terms: 256 + 32p + p2 = -28.66666667 + 256 Combine like terms: -28.66666667 + 256 = 227.33333333 256 + 32p + p2 = 227.33333333 Factor a perfect square on the left side: (p + 16)(p + 16) = 227.33333333 Calculate the square root of the right side: 15.07757717 Break this problem into two subproblems by setting (p + 16) equal to 15.07757717 and -15.07757717.Subproblem 1
p + 16 = 15.07757717 Simplifying p + 16 = 15.07757717 Reorder the terms: 16 + p = 15.07757717 Solving 16 + p = 15.07757717 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + p = 15.07757717 + -16 Combine like terms: 16 + -16 = 0 0 + p = 15.07757717 + -16 p = 15.07757717 + -16 Combine like terms: 15.07757717 + -16 = -0.92242283 p = -0.92242283 Simplifying p = -0.92242283Subproblem 2
p + 16 = -15.07757717 Simplifying p + 16 = -15.07757717 Reorder the terms: 16 + p = -15.07757717 Solving 16 + p = -15.07757717 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + p = -15.07757717 + -16 Combine like terms: 16 + -16 = 0 0 + p = -15.07757717 + -16 p = -15.07757717 + -16 Combine like terms: -15.07757717 + -16 = -31.07757717 p = -31.07757717 Simplifying p = -31.07757717Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.92242283, -31.07757717}Solution
p = {-0.92242283, -31.07757717}
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