1.5+3*6.2+z+z*z=-21

Solution for 1.5+3*6.2+z+z*z=-21 equation:

Simplifying
1.5 + 3 * 6.2 + z + z * z = -21

Multiply 3 * 6.2
1.5 + 18.6 + z + z * z = -21

Multiply z * z
1.5 + 18.6 + z + z2 = -21

Combine like terms: 1.5 + 18.6 = 20.1
20.1 + z + z2 = -21

Solving
20.1 + z + z2 = -21

Solving for variable 'z'.

Reorder the terms:
20.1 + 21 + z + z2 = -21 + 21

Combine like terms: 20.1 + 21 = 41.1
41.1 + z + z2 = -21 + 21

Combine like terms: -21 + 21 = 0
41.1 + z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-41.1' to each side of the equation.
41.1 + z + -41.1 + z2 = 0 + -41.1

Reorder the terms:
41.1 + -41.1 + z + z2 = 0 + -41.1

Combine like terms: 41.1 + -41.1 = 0.0
0.0 + z + z2 = 0 + -41.1
z + z2 = 0 + -41.1

Combine like terms: 0 + -41.1 = -41.1
z + z2 = -41.1

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
z + 0.25 + z2 = -41.1 + 0.25

Reorder the terms:
0.25 + z + z2 = -41.1 + 0.25

Combine like terms: -41.1 + 0.25 = -40.85
0.25 + z + z2 = -40.85

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -40.85

Can't calculate square root of the right side.

The solution to this equation could not be determined.