5x*5x+8x-6=0

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Solution for 5x*5x+8x-6=0 equation:


Simplifying
5x * 5x + 8x + -6 = 0

Reorder the terms for easier multiplication:
5 * 5x * x + 8x + -6 = 0

Multiply 5 * 5
25x * x + 8x + -6 = 0

Multiply x * x
25x2 + 8x + -6 = 0

Reorder the terms:
-6 + 8x + 25x2 = 0

Solving
-6 + 8x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-0.24 + 0.32x + x2 = 0

Move the constant term to the right:

Add '0.24' to each side of the equation.
-0.24 + 0.32x + 0.24 + x2 = 0 + 0.24

Reorder the terms:
-0.24 + 0.24 + 0.32x + x2 = 0 + 0.24

Combine like terms: -0.24 + 0.24 = 0.00
0.00 + 0.32x + x2 = 0 + 0.24
0.32x + x2 = 0 + 0.24

Combine like terms: 0 + 0.24 = 0.24
0.32x + x2 = 0.24

The x term is 0.32x.  Take half its coefficient (0.16).
Square it (0.0256) and add it to both sides.

Add '0.0256' to each side of the equation.
0.32x + 0.0256 + x2 = 0.24 + 0.0256

Reorder the terms:
0.0256 + 0.32x + x2 = 0.24 + 0.0256

Combine like terms: 0.24 + 0.0256 = 0.2656
0.0256 + 0.32x + x2 = 0.2656

Factor a perfect square on the left side:
(x + 0.16)(x + 0.16) = 0.2656

Calculate the square root of the right side: 0.515363949

Break this problem into two subproblems by setting 
(x + 0.16) equal to 0.515363949 and -0.515363949.

Subproblem 1

x + 0.16 = 0.515363949 Simplifying x + 0.16 = 0.515363949 Reorder the terms: 0.16 + x = 0.515363949 Solving 0.16 + x = 0.515363949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.16' to each side of the equation. 0.16 + -0.16 + x = 0.515363949 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + x = 0.515363949 + -0.16 x = 0.515363949 + -0.16 Combine like terms: 0.515363949 + -0.16 = 0.355363949 x = 0.355363949 Simplifying x = 0.355363949

Subproblem 2

x + 0.16 = -0.515363949 Simplifying x + 0.16 = -0.515363949 Reorder the terms: 0.16 + x = -0.515363949 Solving 0.16 + x = -0.515363949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.16' to each side of the equation. 0.16 + -0.16 + x = -0.515363949 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + x = -0.515363949 + -0.16 x = -0.515363949 + -0.16 Combine like terms: -0.515363949 + -0.16 = -0.675363949 x = -0.675363949 Simplifying x = -0.675363949

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.355363949, -0.675363949}

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