25x^2-15x-8=0

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Solution for 25x^2-15x-8=0 equation:


Simplifying
25x2 + -15x + -8 = 0

Reorder the terms:
-8 + -15x + 25x2 = 0

Solving
-8 + -15x + 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 + -0.6x + x2 = 0

Move the constant term to the right:

Add '0.32' to each side of the equation.
-0.32 + -0.6x + 0.32 + x2 = 0 + 0.32

Reorder the terms:
-0.32 + 0.32 + -0.6x + x2 = 0 + 0.32

Combine like terms: -0.32 + 0.32 = 0.00
0.00 + -0.6x + x2 = 0 + 0.32
-0.6x + x2 = 0 + 0.32

Combine like terms: 0 + 0.32 = 0.32
-0.6x + x2 = 0.32

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 0.32 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 0.32 + 0.09

Combine like terms: 0.32 + 0.09 = 0.41
0.09 + -0.6x + x2 = 0.41

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.41

Calculate the square root of the right side: 0.640312424

Break this problem into two subproblems by setting 
(x + -0.3) equal to 0.640312424 and -0.640312424.

Subproblem 1

x + -0.3 = 0.640312424 Simplifying x + -0.3 = 0.640312424 Reorder the terms: -0.3 + x = 0.640312424 Solving -0.3 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.640312424 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.640312424 + 0.3 x = 0.640312424 + 0.3 Combine like terms: 0.640312424 + 0.3 = 0.940312424 x = 0.940312424 Simplifying x = 0.940312424

Subproblem 2

x + -0.3 = -0.640312424 Simplifying x + -0.3 = -0.640312424 Reorder the terms: -0.3 + x = -0.640312424 Solving -0.3 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.640312424 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.640312424 + 0.3 x = -0.640312424 + 0.3 Combine like terms: -0.640312424 + 0.3 = -0.340312424 x = -0.340312424 Simplifying x = -0.340312424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.940312424, -0.340312424}

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