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Simplifying 4p2 + 26p + -40 = 0 Reorder the terms: -40 + 26p + 4p2 = 0 Solving -40 + 26p + 4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 13p + 2p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + 13p + 2p2)' equal to zero and attempt to solve: Simplifying -20 + 13p + 2p2 = 0 Solving -20 + 13p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + 6.5p + p2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 6.5p + 10 + p2 = 0 + 10 Reorder the terms: -10 + 10 + 6.5p + p2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 6.5p + p2 = 0 + 10 6.5p + p2 = 0 + 10 Combine like terms: 0 + 10 = 10 6.5p + p2 = 10 The p term is 6.5p. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5p + 10.5625 + p2 = 10 + 10.5625 Reorder the terms: 10.5625 + 6.5p + p2 = 10 + 10.5625 Combine like terms: 10 + 10.5625 = 20.5625 10.5625 + 6.5p + p2 = 20.5625 Factor a perfect square on the left side: (p + 3.25)(p + 3.25) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (p + 3.25) equal to 4.534589287 and -4.534589287.Subproblem 1
p + 3.25 = 4.534589287 Simplifying p + 3.25 = 4.534589287 Reorder the terms: 3.25 + p = 4.534589287 Solving 3.25 + p = 4.534589287 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + p = 4.534589287 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + p = 4.534589287 + -3.25 p = 4.534589287 + -3.25 Combine like terms: 4.534589287 + -3.25 = 1.284589287 p = 1.284589287 Simplifying p = 1.284589287Subproblem 2
p + 3.25 = -4.534589287 Simplifying p + 3.25 = -4.534589287 Reorder the terms: 3.25 + p = -4.534589287 Solving 3.25 + p = -4.534589287 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + p = -4.534589287 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + p = -4.534589287 + -3.25 p = -4.534589287 + -3.25 Combine like terms: -4.534589287 + -3.25 = -7.784589287 p = -7.784589287 Simplifying p = -7.784589287Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.284589287, -7.784589287}Solution
p = {1.284589287, -7.784589287}
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