3x^2+14x-5=2

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Solution for 3x^2+14x-5=2 equation: 


Simplifying
3x2 + 14x + -5 = 2

Reorder the terms:
-5 + 14x + 3x2 = 2

Solving
-5 + 14x + 3x2 = 2

Solving for variable 'x'.

Reorder the terms:
-5 + -2 + 14x + 3x2 = 2 + -2

Combine like terms: -5 + -2 = -7
-7 + 14x + 3x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-7 + 14x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 4.666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 4.666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 4.666666667x + x2 = 0 + 2.333333333
4.666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
4.666666667x + x2 = 2.333333333

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 = 2.333333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 2.333333333 + 5.444444448

Combine like terms: 2.333333333 + 5.444444448 = 7.777777781
5.444444448 + 4.666666667x + x2 = 7.777777781

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 7.777777781

Calculate the square root of the right side: 2.788866756

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.788866756 and -2.788866756.


Subproblem 1
x + 2.333333334 = 2.788866756

Simplifying
x + 2.333333334 = 2.788866756

Reorder the terms:
2.333333334 + x = 2.788866756

Solving
2.333333334 + x = 2.788866756

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 = 2.788866756 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 2.788866756 + -2.333333334
x = 2.788866756 + -2.333333334

Combine like terms: 2.788866756 + -2.333333334 = 0.455533422
x = 0.455533422

Simplifying
x = 0.455533422


Subproblem 2
x + 2.333333334 = -2.788866756

Simplifying
x + 2.333333334 = -2.788866756

Reorder the terms:
2.333333334 + x = -2.788866756

Solving
2.333333334 + x = -2.788866756

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 = -2.788866756 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -2.788866756 + -2.333333334
x = -2.788866756 + -2.333333334

Combine like terms: -2.788866756 + -2.333333334 = -5.12220009
x = -5.12220009

Simplifying
x = -5.12220009


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.455533422, -5.12220009}

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