4x(1.5+x)=17.6

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Solution for 4x(1.5+x)=17.6 equation: 


Simplifying
4x(1.5 + x) = 17.6
(1.5 * 4x + x * 4x) = 17.6
(6x + 4x2) = 17.6

Solving
6x + 4x2 = 17.6

Solving for variable 'x'.

Reorder the terms:
-17.6 + 6x + 4x2 = 17.6 + -17.6

Combine like terms: 17.6 + -17.6 = 0.0
-17.6 + 6x + 4x2 = 0.0

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

Divide each side by '4'.
-4.4 + 1.5x + x2 = 0.0

Move the constant term to the right:

Add '4.4' to each side of the equation.
-4.4 + 1.5x + 4.4 + x2 = 0.0 + 4.4

Reorder the terms:
-4.4 + 4.4 + 1.5x + x2 = 0.0 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + 1.5x + x2 = 0.0 + 4.4
1.5x + x2 = 0.0 + 4.4

Combine like terms: 0.0 + 4.4 = 4.4
1.5x + x2 = 4.4

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 4.4 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 4.4 + 0.5625

Combine like terms: 4.4 + 0.5625 = 4.9625
0.5625 + 1.5x + x2 = 4.9625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 4.9625

Calculate the square root of the right side: 2.227666941

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.227666941 and -2.227666941.


Subproblem 1
x + 0.75 = 2.227666941

Simplifying
x + 0.75 = 2.227666941

Reorder the terms:
0.75 + x = 2.227666941

Solving
0.75 + x = 2.227666941

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.227666941 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.227666941 + -0.75
x = 2.227666941 + -0.75

Combine like terms: 2.227666941 + -0.75 = 1.477666941
x = 1.477666941

Simplifying
x = 1.477666941


Subproblem 2
x + 0.75 = -2.227666941

Simplifying
x + 0.75 = -2.227666941

Reorder the terms:
0.75 + x = -2.227666941

Solving
0.75 + x = -2.227666941

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.227666941 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.227666941 + -0.75
x = -2.227666941 + -0.75

Combine like terms: -2.227666941 + -0.75 = -2.977666941
x = -2.977666941

Simplifying
x = -2.977666941


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.477666941, -2.977666941}

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