14x^2-11x+2=x^2

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Solution for 14x^2-11x+2=x^2 equation:


Simplifying
14x2 + -11x + 2 = x2

Reorder the terms:
2 + -11x + 14x2 = x2

Solving
2 + -11x + 14x2 = x2

Solving for variable 'x'.

Combine like terms: 14x2 + -1x2 = 13x2
2 + -11x + 13x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -11x + 13x2 = 0

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

Divide each side by '13'.
0.1538461538 + -0.8461538462x + x2 = 0

Move the constant term to the right:

Add '-0.1538461538' to each side of the equation.
0.1538461538 + -0.8461538462x + -0.1538461538 + x2 = 0 + -0.1538461538

Reorder the terms:
0.1538461538 + -0.1538461538 + -0.8461538462x + x2 = 0 + -0.1538461538

Combine like terms: 0.1538461538 + -0.1538461538 = 0.0000000000
0.0000000000 + -0.8461538462x + x2 = 0 + -0.1538461538
-0.8461538462x + x2 = 0 + -0.1538461538

Combine like terms: 0 + -0.1538461538 = -0.1538461538
-0.8461538462x + x2 = -0.1538461538

The x term is -0.8461538462x.  Take half its coefficient (-0.4230769231).
Square it (0.1789940829) and add it to both sides.

Add '0.1789940829' to each side of the equation.
-0.8461538462x + 0.1789940829 + x2 = -0.1538461538 + 0.1789940829

Reorder the terms:
0.1789940829 + -0.8461538462x + x2 = -0.1538461538 + 0.1789940829

Combine like terms: -0.1538461538 + 0.1789940829 = 0.0251479291
0.1789940829 + -0.8461538462x + x2 = 0.0251479291

Factor a perfect square on the left side:
(x + -0.4230769231)(x + -0.4230769231) = 0.0251479291

Calculate the square root of the right side: 0.158580986

Break this problem into two subproblems by setting 
(x + -0.4230769231) equal to 0.158580986 and -0.158580986.

Subproblem 1

x + -0.4230769231 = 0.158580986 Simplifying x + -0.4230769231 = 0.158580986 Reorder the terms: -0.4230769231 + x = 0.158580986 Solving -0.4230769231 + x = 0.158580986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = 0.158580986 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = 0.158580986 + 0.4230769231 x = 0.158580986 + 0.4230769231 Combine like terms: 0.158580986 + 0.4230769231 = 0.5816579091 x = 0.5816579091 Simplifying x = 0.5816579091

Subproblem 2

x + -0.4230769231 = -0.158580986 Simplifying x + -0.4230769231 = -0.158580986 Reorder the terms: -0.4230769231 + x = -0.158580986 Solving -0.4230769231 + x = -0.158580986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = -0.158580986 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = -0.158580986 + 0.4230769231 x = -0.158580986 + 0.4230769231 Combine like terms: -0.158580986 + 0.4230769231 = 0.2644959371 x = 0.2644959371 Simplifying x = 0.2644959371

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5816579091, 0.2644959371}

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