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Simplifying 4p2 + -6p + -5 = 0 Reorder the terms: -5 + -6p + 4p2 = 0 Solving -5 + -6p + 4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -1.5p + p2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.5p + 1.25 + p2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.5p + p2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.5p + p2 = 0 + 1.25 -1.5p + p2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.5p + p2 = 1.25 The p term is -1.5p. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5p + 0.5625 + p2 = 1.25 + 0.5625 Reorder the terms: 0.5625 + -1.5p + p2 = 1.25 + 0.5625 Combine like terms: 1.25 + 0.5625 = 1.8125 0.5625 + -1.5p + p2 = 1.8125 Factor a perfect square on the left side: (p + -0.75)(p + -0.75) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (p + -0.75) equal to 1.346291202 and -1.346291202.Subproblem 1
p + -0.75 = 1.346291202 Simplifying p + -0.75 = 1.346291202 Reorder the terms: -0.75 + p = 1.346291202 Solving -0.75 + p = 1.346291202 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + p = 1.346291202 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + p = 1.346291202 + 0.75 p = 1.346291202 + 0.75 Combine like terms: 1.346291202 + 0.75 = 2.096291202 p = 2.096291202 Simplifying p = 2.096291202Subproblem 2
p + -0.75 = -1.346291202 Simplifying p + -0.75 = -1.346291202 Reorder the terms: -0.75 + p = -1.346291202 Solving -0.75 + p = -1.346291202 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + p = -1.346291202 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + p = -1.346291202 + 0.75 p = -1.346291202 + 0.75 Combine like terms: -1.346291202 + 0.75 = -0.596291202 p = -0.596291202 Simplifying p = -0.596291202Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.096291202, -0.596291202}
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