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Simplifying 5p2 + -7p + -16 = 0 Reorder the terms: -16 + -7p + 5p2 = 0 Solving -16 + -7p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -1.4p + p2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -1.4p + 3.2 + p2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -1.4p + p2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -1.4p + p2 = 0 + 3.2 -1.4p + p2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -1.4p + p2 = 3.2 The p term is -1.4p. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4p + 0.49 + p2 = 3.2 + 0.49 Reorder the terms: 0.49 + -1.4p + p2 = 3.2 + 0.49 Combine like terms: 3.2 + 0.49 = 3.69 0.49 + -1.4p + p2 = 3.69 Factor a perfect square on the left side: (p + -0.7)(p + -0.7) = 3.69 Calculate the square root of the right side: 1.920937271 Break this problem into two subproblems by setting (p + -0.7) equal to 1.920937271 and -1.920937271.Subproblem 1
p + -0.7 = 1.920937271 Simplifying p + -0.7 = 1.920937271 Reorder the terms: -0.7 + p = 1.920937271 Solving -0.7 + p = 1.920937271 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + p = 1.920937271 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + p = 1.920937271 + 0.7 p = 1.920937271 + 0.7 Combine like terms: 1.920937271 + 0.7 = 2.620937271 p = 2.620937271 Simplifying p = 2.620937271Subproblem 2
p + -0.7 = -1.920937271 Simplifying p + -0.7 = -1.920937271 Reorder the terms: -0.7 + p = -1.920937271 Solving -0.7 + p = -1.920937271 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + p = -1.920937271 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + p = -1.920937271 + 0.7 p = -1.920937271 + 0.7 Combine like terms: -1.920937271 + 0.7 = -1.220937271 p = -1.220937271 Simplifying p = -1.220937271Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.620937271, -1.220937271}
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