z^2+6z-4=0

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Solution for z^2+6z-4=0 equation:


Simplifying
z2 + 6z + -4 = 0

Reorder the terms:
-4 + 6z + z2 = 0

Solving
-4 + 6z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6z + 4 + z2 = 0 + 4

Reorder the terms:
-4 + 4 + 6z + z2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6z + z2 = 0 + 4
6z + z2 = 0 + 4

Combine like terms: 0 + 4 = 4
6z + z2 = 4

The z term is 6z.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6z + 9 + z2 = 4 + 9

Reorder the terms:
9 + 6z + z2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + 6z + z2 = 13

Factor a perfect square on the left side:
(z + 3)(z + 3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(z + 3) equal to 3.605551275 and -3.605551275.

Subproblem 1

z + 3 = 3.605551275 Simplifying z + 3 = 3.605551275 Reorder the terms: 3 + z = 3.605551275 Solving 3 + z = 3.605551275 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + z = 3.605551275 + -3 z = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 z = 0.605551275 Simplifying z = 0.605551275

Subproblem 2

z + 3 = -3.605551275 Simplifying z + 3 = -3.605551275 Reorder the terms: 3 + z = -3.605551275 Solving 3 + z = -3.605551275 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + z = -3.605551275 + -3 z = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 z = -6.605551275 Simplifying z = -6.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.605551275, -6.605551275}

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