49z^2+28z+53=0

Solution for 49z^2+28z+53=0 equation:

Simplifying
49z2 + 28z + 53 = 0

Reorder the terms:
53 + 28z + 49z2 = 0

Solving
53 + 28z + 49z2 = 0

Solving for variable 'z'.

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

Divide each side by '49'.
1.081632653 + 0.5714285714z + z2 = 0

Move the constant term to the right:

Add '-1.081632653' to each side of the equation.
1.081632653 + 0.5714285714z + -1.081632653 + z2 = 0 + -1.081632653

Reorder the terms:
1.081632653 + -1.081632653 + 0.5714285714z + z2 = 0 + -1.081632653

Combine like terms: 1.081632653 + -1.081632653 = 0.000000000
0.000000000 + 0.5714285714z + z2 = 0 + -1.081632653
0.5714285714z + z2 = 0 + -1.081632653

Combine like terms: 0 + -1.081632653 = -1.081632653
0.5714285714z + z2 = -1.081632653

The z term is 0.5714285714z.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714z + 0.08163265305 + z2 = -1.081632653 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714z + z2 = -1.081632653 + 0.08163265305

Combine like terms: -1.081632653 + 0.08163265305 = -0.99999999995
0.08163265305 + 0.5714285714z + z2 = -0.99999999995

Factor a perfect square on the left side:
(z + 0.2857142857)(z + 0.2857142857) = -0.99999999995

Can't calculate square root of the right side.

The solution to this equation could not be determined.