5x^2-35x-140=0

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Solution for 5x^2-35x-140=0 equation: 


Simplifying
5x2 + -35x + -140 = 0

Reorder the terms:
-140 + -35x + 5x2 = 0

Solving
-140 + -35x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + -7x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-28 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + -7x + x2 = 0

Solving
-28 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -7x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -7x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -7x + x2 = 0 + 28
-7x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-7x + x2 = 28

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 = 28 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 28 + 12.25

Combine like terms: 28 + 12.25 = 40.25
12.25 + -7x + x2 = 40.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x + -3.5 = 6.34428877

Simplifying
x + -3.5 = 6.34428877

Reorder the terms:
-3.5 + x = 6.34428877

Solving
-3.5 + x = 6.34428877

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 = 6.34428877 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 6.34428877 + 3.5
x = 6.34428877 + 3.5

Combine like terms: 6.34428877 + 3.5 = 9.84428877
x = 9.84428877

Simplifying
x = 9.84428877


Subproblem 2
x + -3.5 = -6.34428877

Simplifying
x + -3.5 = -6.34428877

Reorder the terms:
-3.5 + x = -6.34428877

Solving
-3.5 + x = -6.34428877

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 = -6.34428877 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -6.34428877 + 3.5
x = -6.34428877 + 3.5

Combine like terms: -6.34428877 + 3.5 = -2.84428877
x = -2.84428877

Simplifying
x = -2.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.84428877, -2.84428877}
Solution
x = {9.84428877, -2.84428877}

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