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Simplifying 36 = 4p2 + 4p Reorder the terms: 36 = 4p + 4p2 Solving 36 = 4p + 4p2 Solving for variable 'p'. Reorder the terms: 36 + -4p + -4p2 = 4p + -4p + 4p2 + -4p2 Combine like terms: 4p + -4p = 0 36 + -4p + -4p2 = 0 + 4p2 + -4p2 36 + -4p + -4p2 = 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 36 + -4p + -4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -1p + -1p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -1p + -1p2)' equal to zero and attempt to solve: Simplifying 9 + -1p + -1p2 = 0 Solving 9 + -1p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + p + p2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + p + 9 + p2 = 0 + 9 Reorder the terms: -9 + 9 + p + p2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + p + p2 = 0 + 9 p + p2 = 0 + 9 Combine like terms: 0 + 9 = 9 p + p2 = 9 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. + 0.25 + p2 = 9 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + p2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 1.25 + p2 = 9.25 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (p + 0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
p + 0.5 = 3.041381265 Simplifying p + 0.5 = 3.041381265 Reorder the terms: 0.5 + p = 3.041381265 Solving 0.5 + p = 3.041381265 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 = 3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 3.041381265 + -0.5 p = 3.041381265 + -0.5 Combine like terms: 3.041381265 + -0.5 = 2.541381265 p = 2.541381265 Simplifying p = 2.541381265Subproblem 2
p + 0.5 = -3.041381265 Simplifying p + 0.5 = -3.041381265 Reorder the terms: 0.5 + p = -3.041381265 Solving 0.5 + p = -3.041381265 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 = -3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -3.041381265 + -0.5 p = -3.041381265 + -0.5 Combine like terms: -3.041381265 + -0.5 = -3.541381265 p = -3.541381265 Simplifying p = -3.541381265Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.541381265, -3.541381265}Solution
p = {2.541381265, -3.541381265}
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