27(x^2+5x-280)=0

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Solution for 27(x^2+5x-280)=0 equation: 


Simplifying
27(x2 + 5x + -280) = 0

Reorder the terms:
27(-280 + 5x + x2) = 0
(-280 * 27 + 5x * 27 + x2 * 27) = 0
(-7560 + 135x + 27x2) = 0

Solving
-7560 + 135x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '27'.
27(-280 + 5x + x2) = 0

Ignore the factor 27.

Subproblem 1
Set the factor '(-280 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-280 + 5x + x2 = 0

Solving
-280 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + 5x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 5x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 5x + x2 = 0 + 280
5x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
5x + x2 = 280

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 280 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 280 + 6.25

Combine like terms: 280 + 6.25 = 286.25
6.25 + 5x + x2 = 286.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 286.25

Calculate the square root of the right side: 16.918924316

Break this problem into two subproblems by setting 
(x + 2.5) equal to 16.918924316 and -16.918924316.


Subproblem 1
x + 2.5 = 16.918924316

Simplifying
x + 2.5 = 16.918924316

Reorder the terms:
2.5 + x = 16.918924316

Solving
2.5 + x = 16.918924316

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 16.918924316 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 16.918924316 + -2.5
x = 16.918924316 + -2.5

Combine like terms: 16.918924316 + -2.5 = 14.418924316
x = 14.418924316

Simplifying
x = 14.418924316


Subproblem 2
x + 2.5 = -16.918924316

Simplifying
x + 2.5 = -16.918924316

Reorder the terms:
2.5 + x = -16.918924316

Solving
2.5 + x = -16.918924316

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -16.918924316 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -16.918924316 + -2.5
x = -16.918924316 + -2.5

Combine like terms: -16.918924316 + -2.5 = -19.418924316
x = -19.418924316

Simplifying
x = -19.418924316


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.418924316, -19.418924316}
Solution
x = {14.418924316, -19.418924316}

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