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Simplifying 10p2 + 20p + -64 = -10 Reorder the terms: -64 + 20p + 10p2 = -10 Solving -64 + 20p + 10p2 = -10 Solving for variable 'p'. Reorder the terms: -64 + 10 + 20p + 10p2 = -10 + 10 Combine like terms: -64 + 10 = -54 -54 + 20p + 10p2 = -10 + 10 Combine like terms: -10 + 10 = 0 -54 + 20p + 10p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 10p + 5p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 10p + 5p2)' equal to zero and attempt to solve: Simplifying -27 + 10p + 5p2 = 0 Solving -27 + 10p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + 2p + p2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 2p + 5.4 + p2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 2p + p2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 2p + p2 = 0 + 5.4 2p + p2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 2p + p2 = 5.4 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = 5.4 + 1 Reorder the terms: 1 + 2p + p2 = 5.4 + 1 Combine like terms: 5.4 + 1 = 6.4 1 + 2p + p2 = 6.4 Factor a perfect square on the left side: (p + 1)(p + 1) = 6.4 Calculate the square root of the right side: 2.529822128 Break this problem into two subproblems by setting (p + 1) equal to 2.529822128 and -2.529822128.Subproblem 1
p + 1 = 2.529822128 Simplifying p + 1 = 2.529822128 Reorder the terms: 1 + p = 2.529822128 Solving 1 + p = 2.529822128 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 2.529822128 + -1 Combine like terms: 1 + -1 = 0 0 + p = 2.529822128 + -1 p = 2.529822128 + -1 Combine like terms: 2.529822128 + -1 = 1.529822128 p = 1.529822128 Simplifying p = 1.529822128Subproblem 2
p + 1 = -2.529822128 Simplifying p + 1 = -2.529822128 Reorder the terms: 1 + p = -2.529822128 Solving 1 + p = -2.529822128 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -2.529822128 + -1 Combine like terms: 1 + -1 = 0 0 + p = -2.529822128 + -1 p = -2.529822128 + -1 Combine like terms: -2.529822128 + -1 = -3.529822128 p = -3.529822128 Simplifying p = -3.529822128Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.529822128, -3.529822128}Solution
p = {1.529822128, -3.529822128}
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