z^2+30z+160=

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Solution for z^2+30z+160= equation:


Simplifying
z2 + 30z + 160 = 0

Reorder the terms:
160 + 30z + z2 = 0

Solving
160 + 30z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-160' to each side of the equation.
160 + 30z + -160 + z2 = 0 + -160

Reorder the terms:
160 + -160 + 30z + z2 = 0 + -160

Combine like terms: 160 + -160 = 0
0 + 30z + z2 = 0 + -160
30z + z2 = 0 + -160

Combine like terms: 0 + -160 = -160
30z + z2 = -160

The z term is 30z.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30z + 225 + z2 = -160 + 225

Reorder the terms:
225 + 30z + z2 = -160 + 225

Combine like terms: -160 + 225 = 65
225 + 30z + z2 = 65

Factor a perfect square on the left side:
(z + 15)(z + 15) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(z + 15) equal to 8.062257748 and -8.062257748.

Subproblem 1

z + 15 = 8.062257748 Simplifying z + 15 = 8.062257748 Reorder the terms: 15 + z = 8.062257748 Solving 15 + z = 8.062257748 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + z = 8.062257748 + -15 Combine like terms: 15 + -15 = 0 0 + z = 8.062257748 + -15 z = 8.062257748 + -15 Combine like terms: 8.062257748 + -15 = -6.937742252 z = -6.937742252 Simplifying z = -6.937742252

Subproblem 2

z + 15 = -8.062257748 Simplifying z + 15 = -8.062257748 Reorder the terms: 15 + z = -8.062257748 Solving 15 + z = -8.062257748 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + z = -8.062257748 + -15 Combine like terms: 15 + -15 = 0 0 + z = -8.062257748 + -15 z = -8.062257748 + -15 Combine like terms: -8.062257748 + -15 = -23.062257748 z = -23.062257748 Simplifying z = -23.062257748

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-6.937742252, -23.062257748}

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