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Simplifying 4p2 + 32p = 3 Reorder the terms: 32p + 4p2 = 3 Solving 32p + 4p2 = 3 Solving for variable 'p'. Reorder the terms: -3 + 32p + 4p2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 32p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 8p + p2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 8p + 0.75 + p2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 8p + p2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 8p + p2 = 0 + 0.75 8p + p2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 8p + p2 = 0.75 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 0.75 + 16 Reorder the terms: 16 + 8p + p2 = 0.75 + 16 Combine like terms: 0.75 + 16 = 16.75 16 + 8p + p2 = 16.75 Factor a perfect square on the left side: (p + 4)(p + 4) = 16.75 Calculate the square root of the right side: 4.092676386 Break this problem into two subproblems by setting (p + 4) equal to 4.092676386 and -4.092676386.Subproblem 1
p + 4 = 4.092676386 Simplifying p + 4 = 4.092676386 Reorder the terms: 4 + p = 4.092676386 Solving 4 + p = 4.092676386 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 4.092676386 + -4 Combine like terms: 4 + -4 = 0 0 + p = 4.092676386 + -4 p = 4.092676386 + -4 Combine like terms: 4.092676386 + -4 = 0.092676386 p = 0.092676386 Simplifying p = 0.092676386Subproblem 2
p + 4 = -4.092676386 Simplifying p + 4 = -4.092676386 Reorder the terms: 4 + p = -4.092676386 Solving 4 + p = -4.092676386 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -4.092676386 + -4 Combine like terms: 4 + -4 = 0 0 + p = -4.092676386 + -4 p = -4.092676386 + -4 Combine like terms: -4.092676386 + -4 = -8.092676386 p = -8.092676386 Simplifying p = -8.092676386Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.092676386, -8.092676386}
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