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Simplifying 4p2 + p = 140 Reorder the terms: p + 4p2 = 140 Solving p + 4p2 = 140 Solving for variable 'p'. Reorder the terms: -140 + p + 4p2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -35 + 0.25p + p2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 0.25p + 35 + p2 = 0 + 35 Reorder the terms: -35 + 35 + 0.25p + p2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 0.25p + p2 = 0 + 35 0.25p + p2 = 0 + 35 Combine like terms: 0 + 35 = 35 0.25p + p2 = 35 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25p + 0.25 + p2 = 35 + 0.25 Reorder the terms: 0.25 + 0.25p + p2 = 35 + 0.25 Combine like terms: 35 + 0.25 = 35.25 0.25 + 0.25p + p2 = 35.25 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (p + 0.5) equal to 5.937171044 and -5.937171044.Subproblem 1
p + 0.5 = 5.937171044 Simplifying p + 0.5 = 5.937171044 Reorder the terms: 0.5 + p = 5.937171044 Solving 0.5 + p = 5.937171044 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 5.937171044 + -0.5 p = 5.937171044 + -0.5 Combine like terms: 5.937171044 + -0.5 = 5.437171044 p = 5.437171044 Simplifying p = 5.437171044Subproblem 2
p + 0.5 = -5.937171044 Simplifying p + 0.5 = -5.937171044 Reorder the terms: 0.5 + p = -5.937171044 Solving 0.5 + p = -5.937171044 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -5.937171044 + -0.5 p = -5.937171044 + -0.5 Combine like terms: -5.937171044 + -0.5 = -6.437171044 p = -6.437171044 Simplifying p = -6.437171044Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.437171044, -6.437171044}
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