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Simplifying -11 + 10p(p + 10) = 4 + -5(2p + 11) Reorder the terms: -11 + 10p(10 + p) = 4 + -5(2p + 11) -11 + (10 * 10p + p * 10p) = 4 + -5(2p + 11) -11 + (100p + 10p2) = 4 + -5(2p + 11) Reorder the terms: -11 + 100p + 10p2 = 4 + -5(11 + 2p) -11 + 100p + 10p2 = 4 + (11 * -5 + 2p * -5) -11 + 100p + 10p2 = 4 + (-55 + -10p) Combine like terms: 4 + -55 = -51 -11 + 100p + 10p2 = -51 + -10p Solving -11 + 100p + 10p2 = -51 + -10p Solving for variable 'p'. Reorder the terms: -11 + 51 + 100p + 10p + 10p2 = -51 + -10p + 51 + 10p Combine like terms: -11 + 51 = 40 40 + 100p + 10p + 10p2 = -51 + -10p + 51 + 10p Combine like terms: 100p + 10p = 110p 40 + 110p + 10p2 = -51 + -10p + 51 + 10p Reorder the terms: 40 + 110p + 10p2 = -51 + 51 + -10p + 10p Combine like terms: -51 + 51 = 0 40 + 110p + 10p2 = 0 + -10p + 10p 40 + 110p + 10p2 = -10p + 10p Combine like terms: -10p + 10p = 0 40 + 110p + 10p2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(4 + 11p + p2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(4 + 11p + p2)' equal to zero and attempt to solve: Simplifying 4 + 11p + p2 = 0 Solving 4 + 11p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 11p + -4 + p2 = 0 + -4 Reorder the terms: 4 + -4 + 11p + p2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 11p + p2 = 0 + -4 11p + p2 = 0 + -4 Combine like terms: 0 + -4 = -4 11p + p2 = -4 The p term is 11p. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11p + 30.25 + p2 = -4 + 30.25 Reorder the terms: 30.25 + 11p + p2 = -4 + 30.25 Combine like terms: -4 + 30.25 = 26.25 30.25 + 11p + p2 = 26.25 Factor a perfect square on the left side: (p + 5.5)(p + 5.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (p + 5.5) equal to 5.123475383 and -5.123475383.Subproblem 1
p + 5.5 = 5.123475383 Simplifying p + 5.5 = 5.123475383 Reorder the terms: 5.5 + p = 5.123475383 Solving 5.5 + p = 5.123475383 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + p = 5.123475383 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = 5.123475383 + -5.5 p = 5.123475383 + -5.5 Combine like terms: 5.123475383 + -5.5 = -0.376524617 p = -0.376524617 Simplifying p = -0.376524617Subproblem 2
p + 5.5 = -5.123475383 Simplifying p + 5.5 = -5.123475383 Reorder the terms: 5.5 + p = -5.123475383 Solving 5.5 + p = -5.123475383 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + p = -5.123475383 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = -5.123475383 + -5.5 p = -5.123475383 + -5.5 Combine like terms: -5.123475383 + -5.5 = -10.623475383 p = -10.623475383 Simplifying p = -10.623475383Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.376524617, -10.623475383}Solution
p = {-0.376524617, -10.623475383}
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