4x(4x-3)=148

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Solution for 4x(4x-3)=148 equation: 


Simplifying
4x(4x + -3) = 148

Reorder the terms:
4x(-3 + 4x) = 148
(-3 * 4x + 4x * 4x) = 148
(-12x + 16x2) = 148

Solving
-12x + 16x2 = 148

Solving for variable 'x'.

Reorder the terms:
-148 + -12x + 16x2 = 148 + -148

Combine like terms: 148 + -148 = 0
-148 + -12x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-37 + -3x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-37 + -3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-37 + -3x + 4x2 = 0

Solving
-37 + -3x + 4x2 = 0

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

Divide each side by '4'.
-9.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '9.25' to each side of the equation.
-9.25 + -0.75x + 9.25 + x2 = 0 + 9.25

Reorder the terms:
-9.25 + 9.25 + -0.75x + x2 = 0 + 9.25

Combine like terms: -9.25 + 9.25 = 0.00
0.00 + -0.75x + x2 = 0 + 9.25
-0.75x + x2 = 0 + 9.25

Combine like terms: 0 + 9.25 = 9.25
-0.75x + x2 = 9.25

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 9.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 9.25 + 0.140625

Combine like terms: 9.25 + 0.140625 = 9.390625
0.140625 + -0.75x + x2 = 9.390625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 9.390625

Calculate the square root of the right side: 3.064412668

Break this problem into two subproblems by setting 
(x + -0.375) equal to 3.064412668 and -3.064412668.


Subproblem 1
x + -0.375 = 3.064412668

Simplifying
x + -0.375 = 3.064412668

Reorder the terms:
-0.375 + x = 3.064412668

Solving
-0.375 + x = 3.064412668

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 3.064412668 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 3.064412668 + 0.375
x = 3.064412668 + 0.375

Combine like terms: 3.064412668 + 0.375 = 3.439412668
x = 3.439412668

Simplifying
x = 3.439412668


Subproblem 2
x + -0.375 = -3.064412668

Simplifying
x + -0.375 = -3.064412668

Reorder the terms:
-0.375 + x = -3.064412668

Solving
-0.375 + x = -3.064412668

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -3.064412668 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -3.064412668 + 0.375
x = -3.064412668 + 0.375

Combine like terms: -3.064412668 + 0.375 = -2.689412668
x = -2.689412668

Simplifying
x = -2.689412668


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.439412668, -2.689412668}
Solution
x = {3.439412668, -2.689412668}

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