3x^2+14x-47=0

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Solution for 3x^2+14x-47=0 equation: 


Simplifying
3x2 + 14x + -47 = 0

Reorder the terms:
-47 + 14x + 3x2 = 0

Solving
-47 + 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'.
-15.66666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '15.66666667' to each side of the equation.
-15.66666667 + 4.666666667x + 15.66666667 + x2 = 0 + 15.66666667

Reorder the terms:
-15.66666667 + 15.66666667 + 4.666666667x + x2 = 0 + 15.66666667

Combine like terms: -15.66666667 + 15.66666667 = 0.00000000
0.00000000 + 4.666666667x + x2 = 0 + 15.66666667
4.666666667x + x2 = 0 + 15.66666667

Combine like terms: 0 + 15.66666667 = 15.66666667
4.666666667x + x2 = 15.66666667

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 = 15.66666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 15.66666667 + 5.444444448

Combine like terms: 15.66666667 + 5.444444448 = 21.111111118
5.444444448 + 4.666666667x + x2 = 21.111111118

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 21.111111118

Calculate the square root of the right side: 4.594682918

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 4.594682918 and -4.594682918.


Subproblem 1
x + 2.333333334 = 4.594682918

Simplifying
x + 2.333333334 = 4.594682918

Reorder the terms:
2.333333334 + x = 4.594682918

Solving
2.333333334 + x = 4.594682918

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 = 4.594682918 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 4.594682918 + -2.333333334
x = 4.594682918 + -2.333333334

Combine like terms: 4.594682918 + -2.333333334 = 2.261349584
x = 2.261349584

Simplifying
x = 2.261349584


Subproblem 2
x + 2.333333334 = -4.594682918

Simplifying
x + 2.333333334 = -4.594682918

Reorder the terms:
2.333333334 + x = -4.594682918

Solving
2.333333334 + x = -4.594682918

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 = -4.594682918 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -4.594682918 + -2.333333334
x = -4.594682918 + -2.333333334

Combine like terms: -4.594682918 + -2.333333334 = -6.928016252
x = -6.928016252

Simplifying
x = -6.928016252


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.261349584, -6.928016252}

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