0=3x^2+13x-14

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Solution for 0=3x^2+13x-14 equation:


Simplifying
0 = 3x2 + 13x + -14

Reorder the terms:
0 = -14 + 13x + 3x2

Solving
0 = -14 + 13x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 14 = 14
14 + -13x + -3x2 = -14 + 13x + 3x2 + 14 + -13x + -3x2

Reorder the terms:
14 + -13x + -3x2 = -14 + 14 + 13x + -13x + 3x2 + -3x2

Combine like terms: -14 + 14 = 0
14 + -13x + -3x2 = 0 + 13x + -13x + 3x2 + -3x2
14 + -13x + -3x2 = 13x + -13x + 3x2 + -3x2

Combine like terms: 13x + -13x = 0
14 + -13x + -3x2 = 0 + 3x2 + -3x2
14 + -13x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
14 + -13x + -3x2 = 0

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

Divide each side by '-3'.
-4.666666667 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.333333333x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 4.333333333x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 4.333333333x + x2 = 0 + 4.666666667
4.333333333x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
4.333333333x + x2 = 4.666666667

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 4.666666667 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 4.666666667 + 4.694444446

Combine like terms: 4.666666667 + 4.694444446 = 9.361111113
4.694444446 + 4.333333333x + x2 = 9.361111113

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 9.361111113

Calculate the square root of the right side: 3.059593292

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 3.059593292 and -3.059593292.

Subproblem 1

x + 2.166666667 = 3.059593292 Simplifying x + 2.166666667 = 3.059593292 Reorder the terms: 2.166666667 + x = 3.059593292 Solving 2.166666667 + x = 3.059593292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 3.059593292 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 3.059593292 + -2.166666667 x = 3.059593292 + -2.166666667 Combine like terms: 3.059593292 + -2.166666667 = 0.892926625 x = 0.892926625 Simplifying x = 0.892926625

Subproblem 2

x + 2.166666667 = -3.059593292 Simplifying x + 2.166666667 = -3.059593292 Reorder the terms: 2.166666667 + x = -3.059593292 Solving 2.166666667 + x = -3.059593292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -3.059593292 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -3.059593292 + -2.166666667 x = -3.059593292 + -2.166666667 Combine like terms: -3.059593292 + -2.166666667 = -5.226259959 x = -5.226259959 Simplifying x = -5.226259959

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.892926625, -5.226259959}

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