x^2+69x-1080=0

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Solution for x^2+69x-1080=0 equation: 


Simplifying
x2 + 69x + -1080 = 0

Reorder the terms:
-1080 + 69x + x2 = 0

Solving
-1080 + 69x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1080' to each side of the equation.
-1080 + 69x + 1080 + x2 = 0 + 1080

Reorder the terms:
-1080 + 1080 + 69x + x2 = 0 + 1080

Combine like terms: -1080 + 1080 = 0
0 + 69x + x2 = 0 + 1080
69x + x2 = 0 + 1080

Combine like terms: 0 + 1080 = 1080
69x + x2 = 1080

The x term is 69x.  Take half its coefficient (34.5).
Square it (1190.25) and add it to both sides.

Add '1190.25' to each side of the equation.
69x + 1190.25 + x2 = 1080 + 1190.25

Reorder the terms:
1190.25 + 69x + x2 = 1080 + 1190.25

Combine like terms: 1080 + 1190.25 = 2270.25
1190.25 + 69x + x2 = 2270.25

Factor a perfect square on the left side:
(x + 34.5)(x + 34.5) = 2270.25

Calculate the square root of the right side: 47.647140523

Break this problem into two subproblems by setting 
(x + 34.5) equal to 47.647140523 and -47.647140523.


Subproblem 1
x + 34.5 = 47.647140523

Simplifying
x + 34.5 = 47.647140523

Reorder the terms:
34.5 + x = 47.647140523

Solving
34.5 + x = 47.647140523

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-34.5' to each side of the equation.
34.5 + -34.5 + x = 47.647140523 + -34.5

Combine like terms: 34.5 + -34.5 = 0.0
0.0 + x = 47.647140523 + -34.5
x = 47.647140523 + -34.5

Combine like terms: 47.647140523 + -34.5 = 13.147140523
x = 13.147140523

Simplifying
x = 13.147140523


Subproblem 2
x + 34.5 = -47.647140523

Simplifying
x + 34.5 = -47.647140523

Reorder the terms:
34.5 + x = -47.647140523

Solving
34.5 + x = -47.647140523

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-34.5' to each side of the equation.
34.5 + -34.5 + x = -47.647140523 + -34.5

Combine like terms: 34.5 + -34.5 = 0.0
0.0 + x = -47.647140523 + -34.5
x = -47.647140523 + -34.5

Combine like terms: -47.647140523 + -34.5 = -82.147140523
x = -82.147140523

Simplifying
x = -82.147140523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.147140523, -82.147140523}

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