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Simplifying p2 + -8p * 21 = 6 Reorder the terms for easier multiplication: p2 + -8 * 21p = 6 Multiply -8 * 21 p2 + -168p = 6 Reorder the terms: -168p + p2 = 6 Solving -168p + p2 = 6 Solving for variable 'p'. Reorder the terms: -6 + -168p + p2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -168p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -168p + 6 + p2 = 0 + 6 Reorder the terms: -6 + 6 + -168p + p2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -168p + p2 = 0 + 6 -168p + p2 = 0 + 6 Combine like terms: 0 + 6 = 6 -168p + p2 = 6 The p term is -168p. Take half its coefficient (-84). Square it (7056) and add it to both sides. Add '7056' to each side of the equation. -168p + 7056 + p2 = 6 + 7056 Reorder the terms: 7056 + -168p + p2 = 6 + 7056 Combine like terms: 6 + 7056 = 7062 7056 + -168p + p2 = 7062 Factor a perfect square on the left side: (p + -84)(p + -84) = 7062 Calculate the square root of the right side: 84.035706697 Break this problem into two subproblems by setting (p + -84) equal to 84.035706697 and -84.035706697.Subproblem 1
p + -84 = 84.035706697 Simplifying p + -84 = 84.035706697 Reorder the terms: -84 + p = 84.035706697 Solving -84 + p = 84.035706697 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '84' to each side of the equation. -84 + 84 + p = 84.035706697 + 84 Combine like terms: -84 + 84 = 0 0 + p = 84.035706697 + 84 p = 84.035706697 + 84 Combine like terms: 84.035706697 + 84 = 168.035706697 p = 168.035706697 Simplifying p = 168.035706697Subproblem 2
p + -84 = -84.035706697 Simplifying p + -84 = -84.035706697 Reorder the terms: -84 + p = -84.035706697 Solving -84 + p = -84.035706697 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '84' to each side of the equation. -84 + 84 + p = -84.035706697 + 84 Combine like terms: -84 + 84 = 0 0 + p = -84.035706697 + 84 p = -84.035706697 + 84 Combine like terms: -84.035706697 + 84 = -0.035706697 p = -0.035706697 Simplifying p = -0.035706697Solution
The solution to the problem is based on the solutions from the subproblems. p = {168.035706697, -0.035706697}
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