2x^2=13x+2

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


Simplifying
2x2 = 13x + 2

Reorder the terms:
2x2 = 2 + 13x

Solving
2x2 = 2 + 13x

Solving for variable 'x'.

Reorder the terms:
-2 + -13x + 2x2 = 2 + 13x + -2 + -13x

Reorder the terms:
-2 + -13x + 2x2 = 2 + -2 + 13x + -13x

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

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

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

Divide each side by '2'.
-1 + -6.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -6.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -6.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6.5x + x2 = 0 + 1
-6.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6.5x + x2 = 1

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 1 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 1 + 10.5625

Combine like terms: 1 + 10.5625 = 11.5625
10.5625 + -6.5x + x2 = 11.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.400367627 and -3.400367627.

Subproblem 1

x + -3.25 = 3.400367627 Simplifying x + -3.25 = 3.400367627 Reorder the terms: -3.25 + x = 3.400367627 Solving -3.25 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 3.400367627 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.400367627 + 3.25 x = 3.400367627 + 3.25 Combine like terms: 3.400367627 + 3.25 = 6.650367627 x = 6.650367627 Simplifying x = 6.650367627

Subproblem 2

x + -3.25 = -3.400367627 Simplifying x + -3.25 = -3.400367627 Reorder the terms: -3.25 + x = -3.400367627 Solving -3.25 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -3.400367627 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.400367627 + 3.25 x = -3.400367627 + 3.25 Combine like terms: -3.400367627 + 3.25 = -0.150367627 x = -0.150367627 Simplifying x = -0.150367627

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.650367627, -0.150367627}

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