4(x-2)4x+10=

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Solution for 4(x-2)4x+10= equation: 


Simplifying
4(x + -2) * 4x + 10 = 0

Reorder the terms:
4(-2 + x) * 4x + 10 = 0

Reorder the terms for easier multiplication:
4 * 4x(-2 + x) + 10 = 0

Multiply 4 * 4
16x(-2 + x) + 10 = 0
(-2 * 16x + x * 16x) + 10 = 0
(-32x + 16x2) + 10 = 0

Reorder the terms:
10 + -32x + 16x2 = 0

Solving
10 + -32x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -16x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -16x + 8x2)' equal to zero and attempt to solve:

Simplifying
5 + -16x + 8x2 = 0

Solving
5 + -16x + 8x2 = 0

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

Divide each side by '8'.
0.625 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -2x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -2x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -2x + x2 = 0 + -0.625
-2x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-2x + x2 = -0.625

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 = -0.625 + 1

Reorder the terms:
1 + -2x + x2 = -0.625 + 1

Combine like terms: -0.625 + 1 = 0.375
1 + -2x + x2 = 0.375

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
(x + -1) equal to 0.612372436 and -0.612372436.


Subproblem 1
x + -1 = 0.612372436

Simplifying
x + -1 = 0.612372436

Reorder the terms:
-1 + x = 0.612372436

Solving
-1 + x = 0.612372436

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 = 0.612372436 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.612372436 + 1
x = 0.612372436 + 1

Combine like terms: 0.612372436 + 1 = 1.612372436
x = 1.612372436

Simplifying
x = 1.612372436


Subproblem 2
x + -1 = -0.612372436

Simplifying
x + -1 = -0.612372436

Reorder the terms:
-1 + x = -0.612372436

Solving
-1 + x = -0.612372436

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 = -0.612372436 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.612372436 + 1
x = -0.612372436 + 1

Combine like terms: -0.612372436 + 1 = 0.387627564
x = 0.387627564

Simplifying
x = 0.387627564


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.612372436, 0.387627564}
Solution
x = {1.612372436, 0.387627564}

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