6x^2+x=13

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Solution for 6x^2+x=13 equation:


Simplifying
6x2 + x = 13

Reorder the terms:
x + 6x2 = 13

Solving
x + 6x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + x + 6x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + x + 6x2 = 0

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

Divide each side by '6'.
-2.166666667 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + 0.1666666667x + 2.166666667 + x2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + 0.1666666667x + x2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + 0.1666666667x + x2 = 0 + 2.166666667
0.1666666667x + x2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
0.1666666667x + x2 = 2.166666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667x + 0.25 + x2 = 2.166666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667x + x2 = 2.166666667 + 0.25

Combine like terms: 2.166666667 + 0.25 = 2.416666667
0.25 + 0.1666666667x + x2 = 2.416666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.416666667

Calculate the square root of the right side: 1.554563176

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.554563176 and -1.554563176.

Subproblem 1

x + 0.5 = 1.554563176 Simplifying x + 0.5 = 1.554563176 Reorder the terms: 0.5 + x = 1.554563176 Solving 0.5 + x = 1.554563176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.554563176 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.554563176 + -0.5 x = 1.554563176 + -0.5 Combine like terms: 1.554563176 + -0.5 = 1.054563176 x = 1.054563176 Simplifying x = 1.054563176

Subproblem 2

x + 0.5 = -1.554563176 Simplifying x + 0.5 = -1.554563176 Reorder the terms: 0.5 + x = -1.554563176 Solving 0.5 + x = -1.554563176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.554563176 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.554563176 + -0.5 x = -1.554563176 + -0.5 Combine like terms: -1.554563176 + -0.5 = -2.054563176 x = -2.054563176 Simplifying x = -2.054563176

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.054563176, -2.054563176}

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