x^2+7x-27=0

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Solution for x^2+7x-27=0 equation: 


Simplifying
x2 + 7x + -27 = 0

Reorder the terms:
-27 + 7x + x2 = 0

Solving
-27 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 7x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + 7x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 7x + x2 = 0 + 27
7x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
7x + x2 = 27

The x term is 7x.  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.
7x + 12.25 + x2 = 27 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 27 + 12.25

Combine like terms: 27 + 12.25 = 39.25
12.25 + 7x + x2 = 39.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.264982043 and -6.264982043.


Subproblem 1
x + 3.5 = 6.264982043

Simplifying
x + 3.5 = 6.264982043

Reorder the terms:
3.5 + x = 6.264982043

Solving
3.5 + x = 6.264982043

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 6.264982043 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 6.264982043 + -3.5
x = 6.264982043 + -3.5

Combine like terms: 6.264982043 + -3.5 = 2.764982043
x = 2.764982043

Simplifying
x = 2.764982043


Subproblem 2
x + 3.5 = -6.264982043

Simplifying
x + 3.5 = -6.264982043

Reorder the terms:
3.5 + x = -6.264982043

Solving
3.5 + x = -6.264982043

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -6.264982043 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -6.264982043 + -3.5
x = -6.264982043 + -3.5

Combine like terms: -6.264982043 + -3.5 = -9.764982043
x = -9.764982043

Simplifying
x = -9.764982043


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.764982043, -9.764982043}

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