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Simplifying N(N + -1.2) = 14 Reorder the terms: N(-1.2 + N) = 14 (-1.2 * N + N * N) = 14 (-1.2N + N2) = 14 Solving -1.2N + N2 = 14 Solving for variable 'N'. Reorder the terms: -14 + -1.2N + N2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -1.2N + N2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -1.2N + 14 + N2 = 0 + 14 Reorder the terms: -14 + 14 + -1.2N + N2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1.2N + N2 = 0 + 14 -1.2N + N2 = 0 + 14 Combine like terms: 0 + 14 = 14 -1.2N + N2 = 14 The N term is -1.2N. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2N + 0.36 + N2 = 14 + 0.36 Reorder the terms: 0.36 + -1.2N + N2 = 14 + 0.36 Combine like terms: 14 + 0.36 = 14.36 0.36 + -1.2N + N2 = 14.36 Factor a perfect square on the left side: (N + -0.6)(N + -0.6) = 14.36 Calculate the square root of the right side: 3.789459064 Break this problem into two subproblems by setting (N + -0.6) equal to 3.789459064 and -3.789459064.Subproblem 1
N + -0.6 = 3.789459064 Simplifying N + -0.6 = 3.789459064 Reorder the terms: -0.6 + N = 3.789459064 Solving -0.6 + N = 3.789459064 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + N = 3.789459064 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + N = 3.789459064 + 0.6 N = 3.789459064 + 0.6 Combine like terms: 3.789459064 + 0.6 = 4.389459064 N = 4.389459064 Simplifying N = 4.389459064Subproblem 2
N + -0.6 = -3.789459064 Simplifying N + -0.6 = -3.789459064 Reorder the terms: -0.6 + N = -3.789459064 Solving -0.6 + N = -3.789459064 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + N = -3.789459064 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + N = -3.789459064 + 0.6 N = -3.789459064 + 0.6 Combine like terms: -3.789459064 + 0.6 = -3.189459064 N = -3.189459064 Simplifying N = -3.189459064Solution
The solution to the problem is based on the solutions from the subproblems. N = {4.389459064, -3.189459064}
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