5x^2-40x-140=0

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Solution for 5x^2-40x-140=0 equation: 


Simplifying
5x2 + -40x + -140 = 0

Reorder the terms:
-140 + -40x + 5x2 = 0

Solving
-140 + -40x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + -8x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-28 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + -8x + x2 = 0

Solving
-28 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -8x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -8x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -8x + x2 = 0 + 28
-8x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-8x + x2 = 28

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 28 + 16

Reorder the terms:
16 + -8x + x2 = 28 + 16

Combine like terms: 28 + 16 = 44
16 + -8x + x2 = 44

Factor a perfect square on the left side:
(x + -4)(x + -4) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + -4) equal to 6.633249581 and -6.633249581.


Subproblem 1
x + -4 = 6.633249581

Simplifying
x + -4 = 6.633249581

Reorder the terms:
-4 + x = 6.633249581

Solving
-4 + x = 6.633249581

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 6.633249581 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6.633249581 + 4
x = 6.633249581 + 4

Combine like terms: 6.633249581 + 4 = 10.633249581
x = 10.633249581

Simplifying
x = 10.633249581


Subproblem 2
x + -4 = -6.633249581

Simplifying
x + -4 = -6.633249581

Reorder the terms:
-4 + x = -6.633249581

Solving
-4 + x = -6.633249581

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -6.633249581 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6.633249581 + 4
x = -6.633249581 + 4

Combine like terms: -6.633249581 + 4 = -2.633249581
x = -2.633249581

Simplifying
x = -2.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.633249581, -2.633249581}
Solution
x = {10.633249581, -2.633249581}

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