13=5x^2+x

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Solution for 13=5x^2+x equation:


Simplifying
13 = 5x2 + x

Reorder the terms:
13 = x + 5x2

Solving
13 = x + 5x2

Solving for variable 'x'.

Reorder the terms:
13 + -1x + -5x2 = x + -1x + 5x2 + -5x2

Combine like terms: x + -1x = 0
13 + -1x + -5x2 = 0 + 5x2 + -5x2
13 + -1x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
13 + -1x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2.6 + 0.2x + x2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + 0.2x + 2.6 + x2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 0.2x + x2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 0.2x + x2 = 0 + 2.6
0.2x + x2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
0.2x + x2 = 2.6

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 2.6 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 2.6 + 0.01

Combine like terms: 2.6 + 0.01 = 2.61
0.01 + 0.2x + x2 = 2.61

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 2.61

Calculate the square root of the right side: 1.615549442

Break this problem into two subproblems by setting 
(x + 0.1) equal to 1.615549442 and -1.615549442.

Subproblem 1

x + 0.1 = 1.615549442 Simplifying x + 0.1 = 1.615549442 Reorder the terms: 0.1 + x = 1.615549442 Solving 0.1 + x = 1.615549442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.615549442 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.615549442 + -0.1 x = 1.615549442 + -0.1 Combine like terms: 1.615549442 + -0.1 = 1.515549442 x = 1.515549442 Simplifying x = 1.515549442

Subproblem 2

x + 0.1 = -1.615549442 Simplifying x + 0.1 = -1.615549442 Reorder the terms: 0.1 + x = -1.615549442 Solving 0.1 + x = -1.615549442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.615549442 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.615549442 + -0.1 x = -1.615549442 + -0.1 Combine like terms: -1.615549442 + -0.1 = -1.715549442 x = -1.715549442 Simplifying x = -1.715549442

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.515549442, -1.715549442}

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