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Simplifying n2 + -14n + -56 = 0 Reorder the terms: -56 + -14n + n2 = 0 Solving -56 + -14n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -14n + 56 + n2 = 0 + 56 Reorder the terms: -56 + 56 + -14n + n2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -14n + n2 = 0 + 56 -14n + n2 = 0 + 56 Combine like terms: 0 + 56 = 56 -14n + n2 = 56 The n term is -14n. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14n + 49 + n2 = 56 + 49 Reorder the terms: 49 + -14n + n2 = 56 + 49 Combine like terms: 56 + 49 = 105 49 + -14n + n2 = 105 Factor a perfect square on the left side: (n + -7)(n + -7) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (n + -7) equal to 10.246950766 and -10.246950766.Subproblem 1
n + -7 = 10.246950766 Simplifying n + -7 = 10.246950766 Reorder the terms: -7 + n = 10.246950766 Solving -7 + n = 10.246950766 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = 10.246950766 + 7 Combine like terms: -7 + 7 = 0 0 + n = 10.246950766 + 7 n = 10.246950766 + 7 Combine like terms: 10.246950766 + 7 = 17.246950766 n = 17.246950766 Simplifying n = 17.246950766Subproblem 2
n + -7 = -10.246950766 Simplifying n + -7 = -10.246950766 Reorder the terms: -7 + n = -10.246950766 Solving -7 + n = -10.246950766 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = -10.246950766 + 7 Combine like terms: -7 + 7 = 0 0 + n = -10.246950766 + 7 n = -10.246950766 + 7 Combine like terms: -10.246950766 + 7 = -3.246950766 n = -3.246950766 Simplifying n = -3.246950766Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.246950766, -3.246950766}
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