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Simplifying 2p2 + -14p + -4 = 0 Reorder the terms: -4 + -14p + 2p2 = 0 Solving -4 + -14p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -7p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -7p + p2)' equal to zero and attempt to solve: Simplifying -2 + -7p + p2 = 0 Solving -2 + -7p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -7p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + -7p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7p + p2 = 0 + 2 -7p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7p + p2 = 2 The p term is -7p. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7p + 12.25 + p2 = 2 + 12.25 Reorder the terms: 12.25 + -7p + p2 = 2 + 12.25 Combine like terms: 2 + 12.25 = 14.25 12.25 + -7p + p2 = 14.25 Factor a perfect square on the left side: (p + -3.5)(p + -3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (p + -3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
p + -3.5 = 3.774917218 Simplifying p + -3.5 = 3.774917218 Reorder the terms: -3.5 + p = 3.774917218 Solving -3.5 + p = 3.774917218 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = 3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = 3.774917218 + 3.5 p = 3.774917218 + 3.5 Combine like terms: 3.774917218 + 3.5 = 7.274917218 p = 7.274917218 Simplifying p = 7.274917218Subproblem 2
p + -3.5 = -3.774917218 Simplifying p + -3.5 = -3.774917218 Reorder the terms: -3.5 + p = -3.774917218 Solving -3.5 + p = -3.774917218 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p = -3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = -3.774917218 + 3.5 p = -3.774917218 + 3.5 Combine like terms: -3.774917218 + 3.5 = -0.274917218 p = -0.274917218 Simplifying p = -0.274917218Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.274917218, -0.274917218}Solution
p = {7.274917218, -0.274917218}
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