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Simplifying 5p2 + -10p + -37 = 5 Reorder the terms: -37 + -10p + 5p2 = 5 Solving -37 + -10p + 5p2 = 5 Solving for variable 'p'. Reorder the terms: -37 + -5 + -10p + 5p2 = 5 + -5 Combine like terms: -37 + -5 = -42 -42 + -10p + 5p2 = 5 + -5 Combine like terms: 5 + -5 = 0 -42 + -10p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.4 + -2p + p2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + -2p + 8.4 + p2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + -2p + p2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + -2p + p2 = 0 + 8.4 -2p + p2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 -2p + p2 = 8.4 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 = 8.4 + 1 Reorder the terms: 1 + -2p + p2 = 8.4 + 1 Combine like terms: 8.4 + 1 = 9.4 1 + -2p + p2 = 9.4 Factor a perfect square on the left side: (p + -1)(p + -1) = 9.4 Calculate the square root of the right side: 3.065941943 Break this problem into two subproblems by setting (p + -1) equal to 3.065941943 and -3.065941943.Subproblem 1
p + -1 = 3.065941943 Simplifying p + -1 = 3.065941943 Reorder the terms: -1 + p = 3.065941943 Solving -1 + p = 3.065941943 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 = 3.065941943 + 1 Combine like terms: -1 + 1 = 0 0 + p = 3.065941943 + 1 p = 3.065941943 + 1 Combine like terms: 3.065941943 + 1 = 4.065941943 p = 4.065941943 Simplifying p = 4.065941943Subproblem 2
p + -1 = -3.065941943 Simplifying p + -1 = -3.065941943 Reorder the terms: -1 + p = -3.065941943 Solving -1 + p = -3.065941943 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 = -3.065941943 + 1 Combine like terms: -1 + 1 = 0 0 + p = -3.065941943 + 1 p = -3.065941943 + 1 Combine like terms: -3.065941943 + 1 = -2.065941943 p = -2.065941943 Simplifying p = -2.065941943Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.065941943, -2.065941943}
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