n^2-14n=45

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Solution for n^2-14n=45 equation:


Simplifying
n2 + -14n = 45

Reorder the terms:
-14n + n2 = 45

Solving
-14n + n2 = 45

Solving for variable 'n'.

Reorder the terms:
-45 + -14n + n2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -14n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -14n + 45 + n2 = 0 + 45

Reorder the terms:
-45 + 45 + -14n + n2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -14n + n2 = 0 + 45
-14n + n2 = 0 + 45

Combine like terms: 0 + 45 = 45
-14n + n2 = 45

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 = 45 + 49

Reorder the terms:
49 + -14n + n2 = 45 + 49

Combine like terms: 45 + 49 = 94
49 + -14n + n2 = 94

Factor a perfect square on the left side:
(n + -7)(n + -7) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(n + -7) equal to 9.695359715 and -9.695359715.

Subproblem 1

n + -7 = 9.695359715 Simplifying n + -7 = 9.695359715 Reorder the terms: -7 + n = 9.695359715 Solving -7 + n = 9.695359715 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 = 9.695359715 + 7 Combine like terms: -7 + 7 = 0 0 + n = 9.695359715 + 7 n = 9.695359715 + 7 Combine like terms: 9.695359715 + 7 = 16.695359715 n = 16.695359715 Simplifying n = 16.695359715

Subproblem 2

n + -7 = -9.695359715 Simplifying n + -7 = -9.695359715 Reorder the terms: -7 + n = -9.695359715 Solving -7 + n = -9.695359715 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 = -9.695359715 + 7 Combine like terms: -7 + 7 = 0 0 + n = -9.695359715 + 7 n = -9.695359715 + 7 Combine like terms: -9.695359715 + 7 = -2.695359715 n = -2.695359715 Simplifying n = -2.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. n = {16.695359715, -2.695359715}

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