25x^2+5x-8=

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Solution for 25x^2+5x-8= equation:


Simplifying
25x2 + 5x + -8 = 0

Reorder the terms:
-8 + 5x + 25x2 = 0

Solving
-8 + 5x + 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 + 0.2x + x2 = 0

Move the constant term to the right:

Add '0.32' to each side of the equation.
-0.32 + 0.2x + 0.32 + x2 = 0 + 0.32

Reorder the terms:
-0.32 + 0.32 + 0.2x + x2 = 0 + 0.32

Combine like terms: -0.32 + 0.32 = 0.00
0.00 + 0.2x + x2 = 0 + 0.32
0.2x + x2 = 0 + 0.32

Combine like terms: 0 + 0.32 = 0.32
0.2x + x2 = 0.32

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 0.32 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 0.32 + 0.01

Combine like terms: 0.32 + 0.01 = 0.33
0.01 + 0.2x + x2 = 0.33

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 0.33

Calculate the square root of the right side: 0.574456265

Break this problem into two subproblems by setting 
(x + 0.1) equal to 0.574456265 and -0.574456265.

Subproblem 1

x + 0.1 = 0.574456265 Simplifying x + 0.1 = 0.574456265 Reorder the terms: 0.1 + x = 0.574456265 Solving 0.1 + x = 0.574456265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.574456265 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.574456265 + -0.1 x = 0.574456265 + -0.1 Combine like terms: 0.574456265 + -0.1 = 0.474456265 x = 0.474456265 Simplifying x = 0.474456265

Subproblem 2

x + 0.1 = -0.574456265 Simplifying x + 0.1 = -0.574456265 Reorder the terms: 0.1 + x = -0.574456265 Solving 0.1 + x = -0.574456265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.574456265 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.574456265 + -0.1 x = -0.574456265 + -0.1 Combine like terms: -0.574456265 + -0.1 = -0.674456265 x = -0.674456265 Simplifying x = -0.674456265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.474456265, -0.674456265}

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