5x^2+8x-2=6x

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Solution for 5x^2+8x-2=6x equation:


Simplifying
5x2 + 8x + -2 = 6x

Reorder the terms:
-2 + 8x + 5x2 = 6x

Solving
-2 + 8x + 5x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-2 + 8x + -6x + 5x2 = 6x + -6x

Combine like terms: 8x + -6x = 2x
-2 + 2x + 5x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-2 + 2x + 5x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

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 = 0.4 + 0.04

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

Combine like terms: 0.4 + 0.04 = 0.44
0.04 + 0.4x + x2 = 0.44

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.663324958 and -0.663324958.

Subproblem 1

x + 0.2 = 0.663324958 Simplifying x + 0.2 = 0.663324958 Reorder the terms: 0.2 + x = 0.663324958 Solving 0.2 + x = 0.663324958 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 = 0.663324958 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.663324958 + -0.2 x = 0.663324958 + -0.2 Combine like terms: 0.663324958 + -0.2 = 0.463324958 x = 0.463324958 Simplifying x = 0.463324958

Subproblem 2

x + 0.2 = -0.663324958 Simplifying x + 0.2 = -0.663324958 Reorder the terms: 0.2 + x = -0.663324958 Solving 0.2 + x = -0.663324958 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 = -0.663324958 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.663324958 + -0.2 x = -0.663324958 + -0.2 Combine like terms: -0.663324958 + -0.2 = -0.863324958 x = -0.863324958 Simplifying x = -0.863324958

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.463324958, -0.863324958}

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