21x^2-6-14x=0

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Solution for 21x^2-6-14x=0 equation:


Simplifying
21x2 + -6 + -14x = 0

Reorder the terms:
-6 + -14x + 21x2 = 0

Solving
-6 + -14x + 21x2 = 0

Solving for variable 'x'.

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

Divide each side by '21'.
-0.2857142857 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.6666666667x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.6666666667x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.6666666667x + x2 = 0 + 0.2857142857
-0.6666666667x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.6666666667x + x2 = 0.2857142857

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 0.2857142857 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 0.2857142857 + 0.1111111112

Combine like terms: 0.2857142857 + 0.1111111112 = 0.3968253969
0.1111111112 + -0.6666666667x + x2 = 0.3968253969

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 0.3968253969

Calculate the square root of the right side: 0.629940788

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 0.629940788 and -0.629940788.

Subproblem 1

x + -0.3333333334 = 0.629940788 Simplifying x + -0.3333333334 = 0.629940788 Reorder the terms: -0.3333333334 + x = 0.629940788 Solving -0.3333333334 + x = 0.629940788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.629940788 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.629940788 + 0.3333333334 x = 0.629940788 + 0.3333333334 Combine like terms: 0.629940788 + 0.3333333334 = 0.9632741214 x = 0.9632741214 Simplifying x = 0.9632741214

Subproblem 2

x + -0.3333333334 = -0.629940788 Simplifying x + -0.3333333334 = -0.629940788 Reorder the terms: -0.3333333334 + x = -0.629940788 Solving -0.3333333334 + x = -0.629940788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.629940788 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.629940788 + 0.3333333334 x = -0.629940788 + 0.3333333334 Combine like terms: -0.629940788 + 0.3333333334 = -0.2966074546 x = -0.2966074546 Simplifying x = -0.2966074546

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9632741214, -0.2966074546}

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