z^2+5z+2=

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Solution for z^2+5z+2= equation:


Simplifying
z2 + 5z + 2 = 0

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

Solving
2 + 5z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The z term is 5z.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5z + 6.25 + z2 = -2 + 6.25

Reorder the terms:
6.25 + 5z + z2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + 5z + z2 = 4.25

Factor a perfect square on the left side:
(z + 2.5)(z + 2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(z + 2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

z + 2.5 = 2.061552813 Simplifying z + 2.5 = 2.061552813 Reorder the terms: 2.5 + z = 2.061552813 Solving 2.5 + z = 2.061552813 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = 2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = 2.061552813 + -2.5 z = 2.061552813 + -2.5 Combine like terms: 2.061552813 + -2.5 = -0.438447187 z = -0.438447187 Simplifying z = -0.438447187

Subproblem 2

z + 2.5 = -2.061552813 Simplifying z + 2.5 = -2.061552813 Reorder the terms: 2.5 + z = -2.061552813 Solving 2.5 + z = -2.061552813 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = -2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = -2.061552813 + -2.5 z = -2.061552813 + -2.5 Combine like terms: -2.061552813 + -2.5 = -4.561552813 z = -4.561552813 Simplifying z = -4.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.438447187, -4.561552813}

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