5x^2+2x-13=19

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Solution for 5x^2+2x-13=19 equation:


Simplifying
5x2 + 2x + -13 = 19

Reorder the terms:
-13 + 2x + 5x2 = 19

Solving
-13 + 2x + 5x2 = 19

Solving for variable 'x'.

Reorder the terms:
-13 + -19 + 2x + 5x2 = 19 + -19

Combine like terms: -13 + -19 = -32
-32 + 2x + 5x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-32 + 2x + 5x2 = 0

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

Divide each side by '5'.
-6.4 + 0.4x + x2 = 0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + 0.4x + 6.4 + x2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + 0.4x + x2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + 0.4x + x2 = 0 + 6.4
0.4x + x2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
0.4x + x2 = 6.4

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 6.4 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 6.4 + 0.04

Combine like terms: 6.4 + 0.04 = 6.44
0.04 + 0.4x + x2 = 6.44

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 6.44

Calculate the square root of the right side: 2.537715508

Break this problem into two subproblems by setting 
(x + 0.2) equal to 2.537715508 and -2.537715508.

Subproblem 1

x + 0.2 = 2.537715508 Simplifying x + 0.2 = 2.537715508 Reorder the terms: 0.2 + x = 2.537715508 Solving 0.2 + x = 2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 2.537715508 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.537715508 + -0.2 x = 2.537715508 + -0.2 Combine like terms: 2.537715508 + -0.2 = 2.337715508 x = 2.337715508 Simplifying x = 2.337715508

Subproblem 2

x + 0.2 = -2.537715508 Simplifying x + 0.2 = -2.537715508 Reorder the terms: 0.2 + x = -2.537715508 Solving 0.2 + x = -2.537715508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -2.537715508 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.537715508 + -0.2 x = -2.537715508 + -0.2 Combine like terms: -2.537715508 + -0.2 = -2.737715508 x = -2.737715508 Simplifying x = -2.737715508

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.337715508, -2.737715508}

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