w^2+8w+9=0

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Solution for w^2+8w+9=0 equation:


Simplifying
w2 + 8w + 9 = 0

Reorder the terms:
9 + 8w + w2 = 0

Solving
9 + 8w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 8w + -9 + w2 = 0 + -9

Reorder the terms:
9 + -9 + 8w + w2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8w + w2 = 0 + -9
8w + w2 = 0 + -9

Combine like terms: 0 + -9 = -9
8w + w2 = -9

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

Add '16' to each side of the equation.
8w + 16 + w2 = -9 + 16

Reorder the terms:
16 + 8w + w2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + 8w + w2 = 7

Factor a perfect square on the left side:
(w + 4)(w + 4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(w + 4) equal to 2.645751311 and -2.645751311.

Subproblem 1

w + 4 = 2.645751311 Simplifying w + 4 = 2.645751311 Reorder the terms: 4 + w = 2.645751311 Solving 4 + w = 2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + w = 2.645751311 + -4 w = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 w = -1.354248689 Simplifying w = -1.354248689

Subproblem 2

w + 4 = -2.645751311 Simplifying w + 4 = -2.645751311 Reorder the terms: 4 + w = -2.645751311 Solving 4 + w = -2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + w = -2.645751311 + -4 w = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 w = -6.645751311 Simplifying w = -6.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. w = {-1.354248689, -6.645751311}

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