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Simplifying -1p2 + 4p + 4 = 0 Reorder the terms: 4 + 4p + -1p2 = 0 Solving 4 + 4p + -1p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -4p + p2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4p + 4 + p2 = 0 + 4 Reorder the terms: -4 + 4 + -4p + p2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4p + p2 = 0 + 4 -4p + p2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4p + p2 = 4 The p term is -4p. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4p + 4 + p2 = 4 + 4 Reorder the terms: 4 + -4p + p2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4p + p2 = 8 Factor a perfect square on the left side: (p + -2)(p + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (p + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
p + -2 = 2.828427125 Simplifying p + -2 = 2.828427125 Reorder the terms: -2 + p = 2.828427125 Solving -2 + p = 2.828427125 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + p = 2.828427125 + 2 p = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 p = 4.828427125 Simplifying p = 4.828427125Subproblem 2
p + -2 = -2.828427125 Simplifying p + -2 = -2.828427125 Reorder the terms: -2 + p = -2.828427125 Solving -2 + p = -2.828427125 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + p = -2.828427125 + 2 p = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 p = -0.828427125 Simplifying p = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.828427125, -0.828427125}
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