25x^2+10x-1=0

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Solution for 25x^2+10x-1=0 equation:


Simplifying
25x2 + 10x + -1 = 0

Reorder the terms:
-1 + 10x + 25x2 = 0

Solving
-1 + 10x + 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'.
-0.04 + 0.4x + x2 = 0

Move the constant term to the right:

Add '0.04' to each side of the equation.
-0.04 + 0.4x + 0.04 + x2 = 0 + 0.04

Reorder the terms:
-0.04 + 0.04 + 0.4x + x2 = 0 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + 0.4x + x2 = 0 + 0.04
0.4x + x2 = 0 + 0.04

Combine like terms: 0 + 0.04 = 0.04
0.4x + x2 = 0.04

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 = 0.04 + 0.04

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

Combine like terms: 0.04 + 0.04 = 0.08
0.04 + 0.4x + x2 = 0.08

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.08

Calculate the square root of the right side: 0.282842712

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.282842712 and -0.282842712.

Subproblem 1

x + 0.2 = 0.282842712 Simplifying x + 0.2 = 0.282842712 Reorder the terms: 0.2 + x = 0.282842712 Solving 0.2 + x = 0.282842712 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 = 0.282842712 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.282842712 + -0.2 x = 0.282842712 + -0.2 Combine like terms: 0.282842712 + -0.2 = 0.082842712 x = 0.082842712 Simplifying x = 0.082842712

Subproblem 2

x + 0.2 = -0.282842712 Simplifying x + 0.2 = -0.282842712 Reorder the terms: 0.2 + x = -0.282842712 Solving 0.2 + x = -0.282842712 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 = -0.282842712 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.282842712 + -0.2 x = -0.282842712 + -0.2 Combine like terms: -0.282842712 + -0.2 = -0.482842712 x = -0.482842712 Simplifying x = -0.482842712

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.082842712, -0.482842712}

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