2z^2+4z-10=0

Solution for 2z^2+4z-10=0 equation:

Simplifying
2z2 + 4z + -10 = 0

Reorder the terms:
-10 + 4z + 2z2 = 0

Solving
-10 + 4z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 2z + z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 2z + z2)' equal to zero and attempt to solve:

Simplifying
-5 + 2z + z2 = 0

Solving
-5 + 2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2z + 5 + z2 = 0 + 5

Reorder the terms:
-5 + 5 + 2z + z2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2z + z2 = 0 + 5
2z + z2 = 0 + 5

Combine like terms: 0 + 5 = 5
2z + z2 = 5

The z term is 2z.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2z + 1 + z2 = 5 + 1

Reorder the terms:
1 + 2z + z2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2z + z2 = 6

Factor a perfect square on the left side:
(z + 1)(z + 1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(z + 1) equal to 2.449489743 and -2.449489743.

Subproblem 1
z + 1 = 2.449489743

Simplifying
z + 1 = 2.449489743

Reorder the terms:
1 + z = 2.449489743

Solving
1 + z = 2.449489743

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + z = 2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + z = 2.449489743 + -1
z = 2.449489743 + -1

Combine like terms: 2.449489743 + -1 = 1.449489743
z = 1.449489743

Simplifying
z = 1.449489743

Subproblem 2
z + 1 = -2.449489743

Simplifying
z + 1 = -2.449489743

Reorder the terms:
1 + z = -2.449489743

Solving
1 + z = -2.449489743

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + z = -2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + z = -2.449489743 + -1
z = -2.449489743 + -1

Combine like terms: -2.449489743 + -1 = -3.449489743
z = -3.449489743

Simplifying
z = -3.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.449489743, -3.449489743}
Solution
z = {1.449489743, -3.449489743}