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Simplifying 1p2 + 24p = 43 Reorder the terms: 24p + 1p2 = 43 Solving 24p + 1p2 = 43 Solving for variable 'p'. Reorder the terms: -43 + 24p + 1p2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + 24p + 1p2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 24p + 43 + p2 = 0 + 43 Reorder the terms: -43 + 43 + 24p + p2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 24p + p2 = 0 + 43 24p + p2 = 0 + 43 Combine like terms: 0 + 43 = 43 24p + p2 = 43 The p term is 24p. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24p + 144 + p2 = 43 + 144 Reorder the terms: 144 + 24p + p2 = 43 + 144 Combine like terms: 43 + 144 = 187 144 + 24p + p2 = 187 Factor a perfect square on the left side: (p + 12)(p + 12) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (p + 12) equal to 13.674794331 and -13.674794331.Subproblem 1
p + 12 = 13.674794331 Simplifying p + 12 = 13.674794331 Reorder the terms: 12 + p = 13.674794331 Solving 12 + p = 13.674794331 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + p = 13.674794331 + -12 Combine like terms: 12 + -12 = 0 0 + p = 13.674794331 + -12 p = 13.674794331 + -12 Combine like terms: 13.674794331 + -12 = 1.674794331 p = 1.674794331 Simplifying p = 1.674794331Subproblem 2
p + 12 = -13.674794331 Simplifying p + 12 = -13.674794331 Reorder the terms: 12 + p = -13.674794331 Solving 12 + p = -13.674794331 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + p = -13.674794331 + -12 Combine like terms: 12 + -12 = 0 0 + p = -13.674794331 + -12 p = -13.674794331 + -12 Combine like terms: -13.674794331 + -12 = -25.674794331 p = -25.674794331 Simplifying p = -25.674794331Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.674794331, -25.674794331}
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