3x^2+14x-14=0

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


Simplifying
3x2 + 14x + -14 = 0

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

Solving
-14 + 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'.
-4.666666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = 4.666666667 + 5.444444448

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

Combine like terms: 4.666666667 + 5.444444448 = 10.111111115
5.444444448 + 4.666666667x + x2 = 10.111111115

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 10.111111115

Calculate the square root of the right side: 3.179797339

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 3.179797339 and -3.179797339.

Subproblem 1

x + 2.333333334 = 3.179797339 Simplifying x + 2.333333334 = 3.179797339 Reorder the terms: 2.333333334 + x = 3.179797339 Solving 2.333333334 + x = 3.179797339 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 = 3.179797339 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 3.179797339 + -2.333333334 x = 3.179797339 + -2.333333334 Combine like terms: 3.179797339 + -2.333333334 = 0.846464005 x = 0.846464005 Simplifying x = 0.846464005

Subproblem 2

x + 2.333333334 = -3.179797339 Simplifying x + 2.333333334 = -3.179797339 Reorder the terms: 2.333333334 + x = -3.179797339 Solving 2.333333334 + x = -3.179797339 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 = -3.179797339 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -3.179797339 + -2.333333334 x = -3.179797339 + -2.333333334 Combine like terms: -3.179797339 + -2.333333334 = -5.513130673 x = -5.513130673 Simplifying x = -5.513130673

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.846464005, -5.513130673}

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