25x^2+19x=-1

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Solution for 25x^2+19x=-1 equation:


Simplifying
25x2 + 19x = -1

Reorder the terms:
19x + 25x2 = -1

Solving
19x + 25x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + 19x + 25x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 19x + 25x2 = 0

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

Divide each side by '25'.
0.04 + 0.76x + x2 = 0

Move the constant term to the right:

Add '-0.04' to each side of the equation.
0.04 + 0.76x + -0.04 + x2 = 0 + -0.04

Reorder the terms:
0.04 + -0.04 + 0.76x + x2 = 0 + -0.04

Combine like terms: 0.04 + -0.04 = 0.00
0.00 + 0.76x + x2 = 0 + -0.04
0.76x + x2 = 0 + -0.04

Combine like terms: 0 + -0.04 = -0.04
0.76x + x2 = -0.04

The x term is 0.76x.  Take half its coefficient (0.38).
Square it (0.1444) and add it to both sides.

Add '0.1444' to each side of the equation.
0.76x + 0.1444 + x2 = -0.04 + 0.1444

Reorder the terms:
0.1444 + 0.76x + x2 = -0.04 + 0.1444

Combine like terms: -0.04 + 0.1444 = 0.1044
0.1444 + 0.76x + x2 = 0.1044

Factor a perfect square on the left side:
(x + 0.38)(x + 0.38) = 0.1044

Calculate the square root of the right side: 0.323109888

Break this problem into two subproblems by setting 
(x + 0.38) equal to 0.323109888 and -0.323109888.

Subproblem 1

x + 0.38 = 0.323109888 Simplifying x + 0.38 = 0.323109888 Reorder the terms: 0.38 + x = 0.323109888 Solving 0.38 + x = 0.323109888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.38' to each side of the equation. 0.38 + -0.38 + x = 0.323109888 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + x = 0.323109888 + -0.38 x = 0.323109888 + -0.38 Combine like terms: 0.323109888 + -0.38 = -0.056890112 x = -0.056890112 Simplifying x = -0.056890112

Subproblem 2

x + 0.38 = -0.323109888 Simplifying x + 0.38 = -0.323109888 Reorder the terms: 0.38 + x = -0.323109888 Solving 0.38 + x = -0.323109888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.38' to each side of the equation. 0.38 + -0.38 + x = -0.323109888 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + x = -0.323109888 + -0.38 x = -0.323109888 + -0.38 Combine like terms: -0.323109888 + -0.38 = -0.703109888 x = -0.703109888 Simplifying x = -0.703109888

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.056890112, -0.703109888}

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