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Simplifying 2p2 = 94 + -16p Solving 2p2 = 94 + -16p Solving for variable 'p'. Reorder the terms: -94 + 16p + 2p2 = 94 + -16p + -94 + 16p Reorder the terms: -94 + 16p + 2p2 = 94 + -94 + -16p + 16p Combine like terms: 94 + -94 = 0 -94 + 16p + 2p2 = 0 + -16p + 16p -94 + 16p + 2p2 = -16p + 16p Combine like terms: -16p + 16p = 0 -94 + 16p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 8p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 8p + p2)' equal to zero and attempt to solve: Simplifying -47 + 8p + p2 = 0 Solving -47 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 8p + 47 + p2 = 0 + 47 Reorder the terms: -47 + 47 + 8p + p2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 8p + p2 = 0 + 47 8p + p2 = 0 + 47 Combine like terms: 0 + 47 = 47 8p + p2 = 47 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 47 + 16 Reorder the terms: 16 + 8p + p2 = 47 + 16 Combine like terms: 47 + 16 = 63 16 + 8p + p2 = 63 Factor a perfect square on the left side: (p + 4)(p + 4) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (p + 4) equal to 7.937253933 and -7.937253933.Subproblem 1
p + 4 = 7.937253933 Simplifying p + 4 = 7.937253933 Reorder the terms: 4 + p = 7.937253933 Solving 4 + p = 7.937253933 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 7.937253933 + -4 Combine like terms: 4 + -4 = 0 0 + p = 7.937253933 + -4 p = 7.937253933 + -4 Combine like terms: 7.937253933 + -4 = 3.937253933 p = 3.937253933 Simplifying p = 3.937253933Subproblem 2
p + 4 = -7.937253933 Simplifying p + 4 = -7.937253933 Reorder the terms: 4 + p = -7.937253933 Solving 4 + p = -7.937253933 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -7.937253933 + -4 Combine like terms: 4 + -4 = 0 0 + p = -7.937253933 + -4 p = -7.937253933 + -4 Combine like terms: -7.937253933 + -4 = -11.937253933 p = -11.937253933 Simplifying p = -11.937253933Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.937253933, -11.937253933}Solution
p = {3.937253933, -11.937253933}
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