25x^2-x-8=0

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Solution for 25x^2-x-8=0 equation:


Simplifying
25x2 + -1x + -8 = 0

Reorder the terms:
-8 + -1x + 25x2 = 0

Solving
-8 + -1x + 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'.
-0.32 + -0.04x + x2 = 0

Move the constant term to the right:

Add '0.32' to each side of the equation.
-0.32 + -0.04x + 0.32 + x2 = 0 + 0.32

Reorder the terms:
-0.32 + 0.32 + -0.04x + x2 = 0 + 0.32

Combine like terms: -0.32 + 0.32 = 0.00
0.00 + -0.04x + x2 = 0 + 0.32
-0.04x + x2 = 0 + 0.32

Combine like terms: 0 + 0.32 = 0.32
-0.04x + x2 = 0.32

The x term is -0.04x.  Take half its coefficient (-0.02).
Square it (0.0004) and add it to both sides.

Add '0.0004' to each side of the equation.
-0.04x + 0.0004 + x2 = 0.32 + 0.0004

Reorder the terms:
0.0004 + -0.04x + x2 = 0.32 + 0.0004

Combine like terms: 0.32 + 0.0004 = 0.3204
0.0004 + -0.04x + x2 = 0.3204

Factor a perfect square on the left side:
(x + -0.02)(x + -0.02) = 0.3204

Calculate the square root of the right side: 0.566038868

Break this problem into two subproblems by setting 
(x + -0.02) equal to 0.566038868 and -0.566038868.

Subproblem 1

x + -0.02 = 0.566038868 Simplifying x + -0.02 = 0.566038868 Reorder the terms: -0.02 + x = 0.566038868 Solving -0.02 + x = 0.566038868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = 0.566038868 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 0.566038868 + 0.02 x = 0.566038868 + 0.02 Combine like terms: 0.566038868 + 0.02 = 0.586038868 x = 0.586038868 Simplifying x = 0.586038868

Subproblem 2

x + -0.02 = -0.566038868 Simplifying x + -0.02 = -0.566038868 Reorder the terms: -0.02 + x = -0.566038868 Solving -0.02 + x = -0.566038868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = -0.566038868 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = -0.566038868 + 0.02 x = -0.566038868 + 0.02 Combine like terms: -0.566038868 + 0.02 = -0.546038868 x = -0.546038868 Simplifying x = -0.546038868

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.586038868, -0.546038868}

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