x(4x+8)=10

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Solution for x(4x+8)=10 equation: 


Simplifying
x(4x + 8) = 10

Reorder the terms:
x(8 + 4x) = 10
(8 * x + 4x * x) = 10
(8x + 4x2) = 10

Solving
8x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 8x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 4x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
-5 + 4x + 2x2 = 0

Solving
-5 + 4x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + 2x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 2x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 2x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 2x + x2 = 0 + 2.5
2x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
2x + x2 = 2.5

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 = 2.5 + 1

Reorder the terms:
1 + 2x + x2 = 2.5 + 1

Combine like terms: 2.5 + 1 = 3.5
1 + 2x + x2 = 3.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(x + 1) equal to 1.870828693 and -1.870828693.


Subproblem 1
x + 1 = 1.870828693

Simplifying
x + 1 = 1.870828693

Reorder the terms:
1 + x = 1.870828693

Solving
1 + x = 1.870828693

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 = 1.870828693 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.870828693 + -1
x = 1.870828693 + -1

Combine like terms: 1.870828693 + -1 = 0.870828693
x = 0.870828693

Simplifying
x = 0.870828693


Subproblem 2
x + 1 = -1.870828693

Simplifying
x + 1 = -1.870828693

Reorder the terms:
1 + x = -1.870828693

Solving
1 + x = -1.870828693

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 = -1.870828693 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.870828693 + -1
x = -1.870828693 + -1

Combine like terms: -1.870828693 + -1 = -2.870828693
x = -2.870828693

Simplifying
x = -2.870828693


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.870828693, -2.870828693}
Solution
x = {0.870828693, -2.870828693}

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