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Simplifying 5p2 + -24p + -80 = 0 Reorder the terms: -80 + -24p + 5p2 = 0 Solving -80 + -24p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16 + -4.8p + p2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -4.8p + 16 + p2 = 0 + 16 Reorder the terms: -16 + 16 + -4.8p + p2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -4.8p + p2 = 0 + 16 -4.8p + p2 = 0 + 16 Combine like terms: 0 + 16 = 16 -4.8p + p2 = 16 The p term is -4.8p. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8p + 5.76 + p2 = 16 + 5.76 Reorder the terms: 5.76 + -4.8p + p2 = 16 + 5.76 Combine like terms: 16 + 5.76 = 21.76 5.76 + -4.8p + p2 = 21.76 Factor a perfect square on the left side: (p + -2.4)(p + -2.4) = 21.76 Calculate the square root of the right side: 4.664761516 Break this problem into two subproblems by setting (p + -2.4) equal to 4.664761516 and -4.664761516.Subproblem 1
p + -2.4 = 4.664761516 Simplifying p + -2.4 = 4.664761516 Reorder the terms: -2.4 + p = 4.664761516 Solving -2.4 + p = 4.664761516 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + p = 4.664761516 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + p = 4.664761516 + 2.4 p = 4.664761516 + 2.4 Combine like terms: 4.664761516 + 2.4 = 7.064761516 p = 7.064761516 Simplifying p = 7.064761516Subproblem 2
p + -2.4 = -4.664761516 Simplifying p + -2.4 = -4.664761516 Reorder the terms: -2.4 + p = -4.664761516 Solving -2.4 + p = -4.664761516 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + p = -4.664761516 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + p = -4.664761516 + 2.4 p = -4.664761516 + 2.4 Combine like terms: -4.664761516 + 2.4 = -2.264761516 p = -2.264761516 Simplifying p = -2.264761516Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.064761516, -2.264761516}
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