-3x^2+14x-4=0

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Solution for -3x^2+14x-4=0 equation: 


Simplifying
-3x2 + 14x + -4 = 0

Reorder the terms:
-4 + 14x + -3x2 = 0

Solving
-4 + 14x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -4.666666667x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -4.666666667x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + -1.333333333
-4.666666667x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-4.666666667x + x2 = -1.333333333

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = -1.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -1.333333333 + 5.444444448

Combine like terms: -1.333333333 + 5.444444448 = 4.111111115
5.444444448 + -4.666666667x + x2 = 4.111111115

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 4.111111115

Calculate the square root of the right side: 2.027587511

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.027587511 and -2.027587511.


Subproblem 1
x + -2.333333334 = 2.027587511

Simplifying
x + -2.333333334 = 2.027587511

Reorder the terms:
-2.333333334 + x = 2.027587511

Solving
-2.333333334 + x = 2.027587511

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 2.027587511 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 2.027587511 + 2.333333334
x = 2.027587511 + 2.333333334

Combine like terms: 2.027587511 + 2.333333334 = 4.360920845
x = 4.360920845

Simplifying
x = 4.360920845


Subproblem 2
x + -2.333333334 = -2.027587511

Simplifying
x + -2.333333334 = -2.027587511

Reorder the terms:
-2.333333334 + x = -2.027587511

Solving
-2.333333334 + x = -2.027587511

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -2.027587511 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -2.027587511 + 2.333333334
x = -2.027587511 + 2.333333334

Combine like terms: -2.027587511 + 2.333333334 = 0.305745823
x = 0.305745823

Simplifying
x = 0.305745823


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.360920845, 0.305745823}

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