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Simplifying p2 + -100 = 14p Reorder the terms: -100 + p2 = 14p Solving -100 + p2 = 14p Solving for variable 'p'. Reorder the terms: -100 + -14p + p2 = 14p + -14p Combine like terms: 14p + -14p = 0 -100 + -14p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -14p + 100 + p2 = 0 + 100 Reorder the terms: -100 + 100 + -14p + p2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -14p + p2 = 0 + 100 -14p + p2 = 0 + 100 Combine like terms: 0 + 100 = 100 -14p + p2 = 100 The p term is -14p. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14p + 49 + p2 = 100 + 49 Reorder the terms: 49 + -14p + p2 = 100 + 49 Combine like terms: 100 + 49 = 149 49 + -14p + p2 = 149 Factor a perfect square on the left side: (p + -7)(p + -7) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (p + -7) equal to 12.206555616 and -12.206555616.Subproblem 1
p + -7 = 12.206555616 Simplifying p + -7 = 12.206555616 Reorder the terms: -7 + p = 12.206555616 Solving -7 + p = 12.206555616 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = 12.206555616 + 7 Combine like terms: -7 + 7 = 0 0 + p = 12.206555616 + 7 p = 12.206555616 + 7 Combine like terms: 12.206555616 + 7 = 19.206555616 p = 19.206555616 Simplifying p = 19.206555616Subproblem 2
p + -7 = -12.206555616 Simplifying p + -7 = -12.206555616 Reorder the terms: -7 + p = -12.206555616 Solving -7 + p = -12.206555616 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + p = -12.206555616 + 7 Combine like terms: -7 + 7 = 0 0 + p = -12.206555616 + 7 p = -12.206555616 + 7 Combine like terms: -12.206555616 + 7 = -5.206555616 p = -5.206555616 Simplifying p = -5.206555616Solution
The solution to the problem is based on the solutions from the subproblems. p = {19.206555616, -5.206555616}
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