z^2+8z-45=0

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Solution for z^2+8z-45=0 equation:


Simplifying
z2 + 8z + -45 = 0

Reorder the terms:
-45 + 8z + z2 = 0

Solving
-45 + 8z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 8z + 45 + z2 = 0 + 45

Reorder the terms:
-45 + 45 + 8z + z2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 8z + z2 = 0 + 45
8z + z2 = 0 + 45

Combine like terms: 0 + 45 = 45
8z + z2 = 45

The z term is 8z.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8z + 16 + z2 = 45 + 16

Reorder the terms:
16 + 8z + z2 = 45 + 16

Combine like terms: 45 + 16 = 61
16 + 8z + z2 = 61

Factor a perfect square on the left side:
(z + 4)(z + 4) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(z + 4) equal to 7.810249676 and -7.810249676.

Subproblem 1

z + 4 = 7.810249676 Simplifying z + 4 = 7.810249676 Reorder the terms: 4 + z = 7.810249676 Solving 4 + z = 7.810249676 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 7.810249676 + -4 Combine like terms: 4 + -4 = 0 0 + z = 7.810249676 + -4 z = 7.810249676 + -4 Combine like terms: 7.810249676 + -4 = 3.810249676 z = 3.810249676 Simplifying z = 3.810249676

Subproblem 2

z + 4 = -7.810249676 Simplifying z + 4 = -7.810249676 Reorder the terms: 4 + z = -7.810249676 Solving 4 + z = -7.810249676 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = -7.810249676 + -4 Combine like terms: 4 + -4 = 0 0 + z = -7.810249676 + -4 z = -7.810249676 + -4 Combine like terms: -7.810249676 + -4 = -11.810249676 z = -11.810249676 Simplifying z = -11.810249676

Solution

The solution to the problem is based on the solutions from the subproblems. z = {3.810249676, -11.810249676}

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