5x^2+34x+61=0

Solution for 5x^2+34x+61=0 equation:

Simplifying
5x2 + 34x + 61 = 0

Reorder the terms:
61 + 34x + 5x2 = 0

Solving
61 + 34x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
12.2 + 6.8x + x2 = 0

Move the constant term to the right:

Add '-12.2' to each side of the equation.
12.2 + 6.8x + -12.2 + x2 = 0 + -12.2

Reorder the terms:
12.2 + -12.2 + 6.8x + x2 = 0 + -12.2

Combine like terms: 12.2 + -12.2 = 0.0
0.0 + 6.8x + x2 = 0 + -12.2
6.8x + x2 = 0 + -12.2

Combine like terms: 0 + -12.2 = -12.2
6.8x + x2 = -12.2

The x term is 6.8x.  Take half its coefficient (3.4).
Square it (11.56) and add it to both sides.

Add '11.56' to each side of the equation.
6.8x + 11.56 + x2 = -12.2 + 11.56

Reorder the terms:
11.56 + 6.8x + x2 = -12.2 + 11.56

Combine like terms: -12.2 + 11.56 = -0.64
11.56 + 6.8x + x2 = -0.64

Factor a perfect square on the left side:
(x + 3.4)(x + 3.4) = -0.64

Can't calculate square root of the right side.

The solution to this equation could not be determined.