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Simplifying -50p2 + -30p + 160 = 0 Reorder the terms: 160 + -30p + -50p2 = 0 Solving 160 + -30p + -50p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '10'. 10(16 + -3p + -5p2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(16 + -3p + -5p2)' equal to zero and attempt to solve: Simplifying 16 + -3p + -5p2 = 0 Solving 16 + -3p + -5p2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.2 + 0.6p + p2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 0.6p + 3.2 + p2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 0.6p + p2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 0.6p + p2 = 0 + 3.2 0.6p + p2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 0.6p + p2 = 3.2 The p term is 0.6p. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6p + 0.09 + p2 = 3.2 + 0.09 Reorder the terms: 0.09 + 0.6p + p2 = 3.2 + 0.09 Combine like terms: 3.2 + 0.09 = 3.29 0.09 + 0.6p + p2 = 3.29 Factor a perfect square on the left side: (p + 0.3)(p + 0.3) = 3.29 Calculate the square root of the right side: 1.813835715 Break this problem into two subproblems by setting (p + 0.3) equal to 1.813835715 and -1.813835715.Subproblem 1
p + 0.3 = 1.813835715 Simplifying p + 0.3 = 1.813835715 Reorder the terms: 0.3 + p = 1.813835715 Solving 0.3 + p = 1.813835715 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + p = 1.813835715 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + p = 1.813835715 + -0.3 p = 1.813835715 + -0.3 Combine like terms: 1.813835715 + -0.3 = 1.513835715 p = 1.513835715 Simplifying p = 1.513835715Subproblem 2
p + 0.3 = -1.813835715 Simplifying p + 0.3 = -1.813835715 Reorder the terms: 0.3 + p = -1.813835715 Solving 0.3 + p = -1.813835715 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + p = -1.813835715 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + p = -1.813835715 + -0.3 p = -1.813835715 + -0.3 Combine like terms: -1.813835715 + -0.3 = -2.113835715 p = -2.113835715 Simplifying p = -2.113835715Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.513835715, -2.113835715}Solution
p = {1.513835715, -2.113835715}
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