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Simplifying 5p2 + -73p + 241 = 3p Reorder the terms: 241 + -73p + 5p2 = 3p Solving 241 + -73p + 5p2 = 3p Solving for variable 'p'. Reorder the terms: 241 + -73p + -3p + 5p2 = 3p + -3p Combine like terms: -73p + -3p = -76p 241 + -76p + 5p2 = 3p + -3p Combine like terms: 3p + -3p = 0 241 + -76p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 48.2 + -15.2p + p2 = 0 Move the constant term to the right: Add '-48.2' to each side of the equation. 48.2 + -15.2p + -48.2 + p2 = 0 + -48.2 Reorder the terms: 48.2 + -48.2 + -15.2p + p2 = 0 + -48.2 Combine like terms: 48.2 + -48.2 = 0.0 0.0 + -15.2p + p2 = 0 + -48.2 -15.2p + p2 = 0 + -48.2 Combine like terms: 0 + -48.2 = -48.2 -15.2p + p2 = -48.2 The p term is -15.2p. Take half its coefficient (-7.6). Square it (57.76) and add it to both sides. Add '57.76' to each side of the equation. -15.2p + 57.76 + p2 = -48.2 + 57.76 Reorder the terms: 57.76 + -15.2p + p2 = -48.2 + 57.76 Combine like terms: -48.2 + 57.76 = 9.56 57.76 + -15.2p + p2 = 9.56 Factor a perfect square on the left side: (p + -7.6)(p + -7.6) = 9.56 Calculate the square root of the right side: 3.091924967 Break this problem into two subproblems by setting (p + -7.6) equal to 3.091924967 and -3.091924967.Subproblem 1
p + -7.6 = 3.091924967 Simplifying p + -7.6 = 3.091924967 Reorder the terms: -7.6 + p = 3.091924967 Solving -7.6 + p = 3.091924967 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.6' to each side of the equation. -7.6 + 7.6 + p = 3.091924967 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + p = 3.091924967 + 7.6 p = 3.091924967 + 7.6 Combine like terms: 3.091924967 + 7.6 = 10.691924967 p = 10.691924967 Simplifying p = 10.691924967Subproblem 2
p + -7.6 = -3.091924967 Simplifying p + -7.6 = -3.091924967 Reorder the terms: -7.6 + p = -3.091924967 Solving -7.6 + p = -3.091924967 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7.6' to each side of the equation. -7.6 + 7.6 + p = -3.091924967 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + p = -3.091924967 + 7.6 p = -3.091924967 + 7.6 Combine like terms: -3.091924967 + 7.6 = 4.508075033 p = 4.508075033 Simplifying p = 4.508075033Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.691924967, 4.508075033}
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