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Simplifying 4p2 = 75 + 8p Solving 4p2 = 75 + 8p Solving for variable 'p'. Reorder the terms: -75 + -8p + 4p2 = 75 + 8p + -75 + -8p Reorder the terms: -75 + -8p + 4p2 = 75 + -75 + 8p + -8p Combine like terms: 75 + -75 = 0 -75 + -8p + 4p2 = 0 + 8p + -8p -75 + -8p + 4p2 = 8p + -8p Combine like terms: 8p + -8p = 0 -75 + -8p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + -2p + p2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -2p + 18.75 + p2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -2p + p2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -2p + p2 = 0 + 18.75 -2p + p2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -2p + p2 = 18.75 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 = 18.75 + 1 Reorder the terms: 1 + -2p + p2 = 18.75 + 1 Combine like terms: 18.75 + 1 = 19.75 1 + -2p + p2 = 19.75 Factor a perfect square on the left side: (p + -1)(p + -1) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (p + -1) equal to 4.444097209 and -4.444097209.Subproblem 1
p + -1 = 4.444097209 Simplifying p + -1 = 4.444097209 Reorder the terms: -1 + p = 4.444097209 Solving -1 + p = 4.444097209 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 = 4.444097209 + 1 Combine like terms: -1 + 1 = 0 0 + p = 4.444097209 + 1 p = 4.444097209 + 1 Combine like terms: 4.444097209 + 1 = 5.444097209 p = 5.444097209 Simplifying p = 5.444097209Subproblem 2
p + -1 = -4.444097209 Simplifying p + -1 = -4.444097209 Reorder the terms: -1 + p = -4.444097209 Solving -1 + p = -4.444097209 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 = -4.444097209 + 1 Combine like terms: -1 + 1 = 0 0 + p = -4.444097209 + 1 p = -4.444097209 + 1 Combine like terms: -4.444097209 + 1 = -3.444097209 p = -3.444097209 Simplifying p = -3.444097209Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.444097209, -3.444097209}
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