z^2+9z+15=

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Solution for z^2+9z+15= equation:


Simplifying
z2 + 9z + 15 = 0

Reorder the terms:
15 + 9z + z2 = 0

Solving
15 + 9z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 9z + -15 + z2 = 0 + -15

Reorder the terms:
15 + -15 + 9z + z2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 9z + z2 = 0 + -15
9z + z2 = 0 + -15

Combine like terms: 0 + -15 = -15
9z + z2 = -15

The z term is 9z.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9z + 20.25 + z2 = -15 + 20.25

Reorder the terms:
20.25 + 9z + z2 = -15 + 20.25

Combine like terms: -15 + 20.25 = 5.25
20.25 + 9z + z2 = 5.25

Factor a perfect square on the left side:
(z + 4.5)(z + 4.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(z + 4.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

z + 4.5 = 2.291287847 Simplifying z + 4.5 = 2.291287847 Reorder the terms: 4.5 + z = 2.291287847 Solving 4.5 + z = 2.291287847 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = 2.291287847 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = 2.291287847 + -4.5 z = 2.291287847 + -4.5 Combine like terms: 2.291287847 + -4.5 = -2.208712153 z = -2.208712153 Simplifying z = -2.208712153

Subproblem 2

z + 4.5 = -2.291287847 Simplifying z + 4.5 = -2.291287847 Reorder the terms: 4.5 + z = -2.291287847 Solving 4.5 + z = -2.291287847 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = -2.291287847 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = -2.291287847 + -4.5 z = -2.291287847 + -4.5 Combine like terms: -2.291287847 + -4.5 = -6.791287847 z = -6.791287847 Simplifying z = -6.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-2.208712153, -6.791287847}

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