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Simplifying (n + -7)(n + -7) = 2n Reorder the terms: (-7 + n)(n + -7) = 2n Reorder the terms: (-7 + n)(-7 + n) = 2n Multiply (-7 + n) * (-7 + n) (-7(-7 + n) + n(-7 + n)) = 2n ((-7 * -7 + n * -7) + n(-7 + n)) = 2n ((49 + -7n) + n(-7 + n)) = 2n (49 + -7n + (-7 * n + n * n)) = 2n (49 + -7n + (-7n + n2)) = 2n Combine like terms: -7n + -7n = -14n (49 + -14n + n2) = 2n Solving 49 + -14n + n2 = 2n Solving for variable 'n'. Reorder the terms: 49 + -14n + -2n + n2 = 2n + -2n Combine like terms: -14n + -2n = -16n 49 + -16n + n2 = 2n + -2n Combine like terms: 2n + -2n = 0 49 + -16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -16n + -49 + n2 = 0 + -49 Reorder the terms: 49 + -49 + -16n + n2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -16n + n2 = 0 + -49 -16n + n2 = 0 + -49 Combine like terms: 0 + -49 = -49 -16n + n2 = -49 The n term is -16n. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16n + 64 + n2 = -49 + 64 Reorder the terms: 64 + -16n + n2 = -49 + 64 Combine like terms: -49 + 64 = 15 64 + -16n + n2 = 15 Factor a perfect square on the left side: (n + -8)(n + -8) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (n + -8) equal to 3.872983346 and -3.872983346.Subproblem 1
n + -8 = 3.872983346 Simplifying n + -8 = 3.872983346 Reorder the terms: -8 + n = 3.872983346 Solving -8 + n = 3.872983346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = 3.872983346 + 8 Combine like terms: -8 + 8 = 0 0 + n = 3.872983346 + 8 n = 3.872983346 + 8 Combine like terms: 3.872983346 + 8 = 11.872983346 n = 11.872983346 Simplifying n = 11.872983346Subproblem 2
n + -8 = -3.872983346 Simplifying n + -8 = -3.872983346 Reorder the terms: -8 + n = -3.872983346 Solving -8 + n = -3.872983346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = -3.872983346 + 8 Combine like terms: -8 + 8 = 0 0 + n = -3.872983346 + 8 n = -3.872983346 + 8 Combine like terms: -3.872983346 + 8 = 4.127016654 n = 4.127016654 Simplifying n = 4.127016654Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.872983346, 4.127016654}
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