70=n^2+7n

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Solution for 70=n^2+7n equation:


Simplifying
70 = n2 + 7n

Reorder the terms:
70 = 7n + n2

Solving
70 = 7n + n2

Solving for variable 'n'.

Reorder the terms:
70 + -7n + -1n2 = 7n + -7n + n2 + -1n2

Combine like terms: 7n + -7n = 0
70 + -7n + -1n2 = 0 + n2 + -1n2
70 + -7n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
70 + -7n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-70 + 7n + n2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 7n + 70 + n2 = 0 + 70

Reorder the terms:
-70 + 70 + 7n + n2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 7n + n2 = 0 + 70
7n + n2 = 0 + 70

Combine like terms: 0 + 70 = 70
7n + n2 = 70

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = 70 + 12.25

Reorder the terms:
12.25 + 7n + n2 = 70 + 12.25

Combine like terms: 70 + 12.25 = 82.25
12.25 + 7n + n2 = 82.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(n + 3.5) equal to 9.069178574 and -9.069178574.

Subproblem 1

n + 3.5 = 9.069178574 Simplifying n + 3.5 = 9.069178574 Reorder the terms: 3.5 + n = 9.069178574 Solving 3.5 + n = 9.069178574 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 9.069178574 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 9.069178574 + -3.5 n = 9.069178574 + -3.5 Combine like terms: 9.069178574 + -3.5 = 5.569178574 n = 5.569178574 Simplifying n = 5.569178574

Subproblem 2

n + 3.5 = -9.069178574 Simplifying n + 3.5 = -9.069178574 Reorder the terms: 3.5 + n = -9.069178574 Solving 3.5 + n = -9.069178574 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -9.069178574 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -9.069178574 + -3.5 n = -9.069178574 + -3.5 Combine like terms: -9.069178574 + -3.5 = -12.569178574 n = -12.569178574 Simplifying n = -12.569178574

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.569178574, -12.569178574}

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