140-4x(4x+8)=0

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Solution for 140-4x(4x+8)=0 equation: 


Simplifying
140 + -4x(4x + 8) = 0

Reorder the terms:
140 + -4x(8 + 4x) = 0
140 + (8 * -4x + 4x * -4x) = 0
140 + (-32x + -16x2) = 0

Solving
140 + -32x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(35 + -8x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(35 + -8x + -4x2)' equal to zero and attempt to solve:

Simplifying
35 + -8x + -4x2 = 0

Solving
35 + -8x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-8.75 + 2x + x2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + 2x + 8.75 + x2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + 2x + x2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + 2x + x2 = 0 + 8.75
2x + x2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
2x + x2 = 8.75

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 8.75 + 1

Reorder the terms:
1 + 2x + x2 = 8.75 + 1

Combine like terms: 8.75 + 1 = 9.75
1 + 2x + x2 = 9.75

Factor a perfect square on the left side:
(x + 1)(x + 1) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + 1) equal to 3.122498999 and -3.122498999.


Subproblem 1
x + 1 = 3.122498999

Simplifying
x + 1 = 3.122498999

Reorder the terms:
1 + x = 3.122498999

Solving
1 + x = 3.122498999

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.122498999 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.122498999 + -1
x = 3.122498999 + -1

Combine like terms: 3.122498999 + -1 = 2.122498999
x = 2.122498999

Simplifying
x = 2.122498999


Subproblem 2
x + 1 = -3.122498999

Simplifying
x + 1 = -3.122498999

Reorder the terms:
1 + x = -3.122498999

Solving
1 + x = -3.122498999

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.122498999 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.122498999 + -1
x = -3.122498999 + -1

Combine like terms: -3.122498999 + -1 = -4.122498999
x = -4.122498999

Simplifying
x = -4.122498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.122498999, -4.122498999}
Solution
x = {2.122498999, -4.122498999}

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