4x(1.2x-1.8)=71

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Solution for 4x(1.2x-1.8)=71 equation: 


Simplifying
4x(1.2x + -1.8) = 71

Reorder the terms:
4x(-1.8 + 1.2x) = 71
(-1.8 * 4x + 1.2x * 4x) = 71
(-7.2x + 4.8x2) = 71

Solving
-7.2x + 4.8x2 = 71

Solving for variable 'x'.

Reorder the terms:
-71 + -7.2x + 4.8x2 = 71 + -71

Combine like terms: 71 + -71 = 0
-71 + -7.2x + 4.8x2 = 0

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

Divide each side by '4.8'.
-14.79166667 + -1.5x + x2 = 0

Move the constant term to the right:

Add '14.79166667' to each side of the equation.
-14.79166667 + -1.5x + 14.79166667 + x2 = 0 + 14.79166667

Reorder the terms:
-14.79166667 + 14.79166667 + -1.5x + x2 = 0 + 14.79166667

Combine like terms: -14.79166667 + 14.79166667 = 0.00000000
0.00000000 + -1.5x + x2 = 0 + 14.79166667
-1.5x + x2 = 0 + 14.79166667

Combine like terms: 0 + 14.79166667 = 14.79166667
-1.5x + x2 = 14.79166667

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 = 14.79166667 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 14.79166667 + 0.5625

Combine like terms: 14.79166667 + 0.5625 = 15.35416667
0.5625 + -1.5x + x2 = 15.35416667

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 15.35416667

Calculate the square root of the right side: 3.918439316

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.918439316 and -3.918439316.


Subproblem 1
x + -0.75 = 3.918439316

Simplifying
x + -0.75 = 3.918439316

Reorder the terms:
-0.75 + x = 3.918439316

Solving
-0.75 + x = 3.918439316

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 = 3.918439316 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 3.918439316 + 0.75
x = 3.918439316 + 0.75

Combine like terms: 3.918439316 + 0.75 = 4.668439316
x = 4.668439316

Simplifying
x = 4.668439316


Subproblem 2
x + -0.75 = -3.918439316

Simplifying
x + -0.75 = -3.918439316

Reorder the terms:
-0.75 + x = -3.918439316

Solving
-0.75 + x = -3.918439316

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 = -3.918439316 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -3.918439316 + 0.75
x = -3.918439316 + 0.75

Combine like terms: -3.918439316 + 0.75 = -3.168439316
x = -3.168439316

Simplifying
x = -3.168439316


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.668439316, -3.168439316}

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