5x^2-35x-55=0

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Solution for 5x^2-35x-55=0 equation: 


Simplifying
5x2 + -35x + -55 = 0

Reorder the terms:
-55 + -35x + 5x2 = 0

Solving
-55 + -35x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-11 + -7x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-11 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-11 + -7x + x2 = 0

Solving
-11 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -7x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -7x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -7x + x2 = 0 + 11
-7x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-7x + x2 = 11

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 = 11 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 11 + 12.25

Combine like terms: 11 + 12.25 = 23.25
12.25 + -7x + x2 = 23.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.82182538 and -4.82182538.


Subproblem 1
x + -3.5 = 4.82182538

Simplifying
x + -3.5 = 4.82182538

Reorder the terms:
-3.5 + x = 4.82182538

Solving
-3.5 + x = 4.82182538

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 = 4.82182538 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.82182538 + 3.5
x = 4.82182538 + 3.5

Combine like terms: 4.82182538 + 3.5 = 8.32182538
x = 8.32182538

Simplifying
x = 8.32182538


Subproblem 2
x + -3.5 = -4.82182538

Simplifying
x + -3.5 = -4.82182538

Reorder the terms:
-3.5 + x = -4.82182538

Solving
-3.5 + x = -4.82182538

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 = -4.82182538 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.82182538 + 3.5
x = -4.82182538 + 3.5

Combine like terms: -4.82182538 + 3.5 = -1.32182538
x = -1.32182538

Simplifying
x = -1.32182538


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.32182538, -1.32182538}
Solution
x = {8.32182538, -1.32182538}

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