w^2+3w+9=20

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Solution for w^2+3w+9=20 equation:


Simplifying
w2 + 3w + 9 = 20

Reorder the terms:
9 + 3w + w2 = 20

Solving
9 + 3w + w2 = 20

Solving for variable 'w'.

Reorder the terms:
9 + -20 + 3w + w2 = 20 + -20

Combine like terms: 9 + -20 = -11
-11 + 3w + w2 = 20 + -20

Combine like terms: 20 + -20 = 0
-11 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 3w + 11 + w2 = 0 + 11

Reorder the terms:
-11 + 11 + 3w + w2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 3w + w2 = 0 + 11
3w + w2 = 0 + 11

Combine like terms: 0 + 11 = 11
3w + w2 = 11

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 11 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 11 + 2.25

Combine like terms: 11 + 2.25 = 13.25
2.25 + 3w + w2 = 13.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(w + 1.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

w + 1.5 = 3.640054945 Simplifying w + 1.5 = 3.640054945 Reorder the terms: 1.5 + w = 3.640054945 Solving 1.5 + w = 3.640054945 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 3.640054945 + -1.5 w = 3.640054945 + -1.5 Combine like terms: 3.640054945 + -1.5 = 2.140054945 w = 2.140054945 Simplifying w = 2.140054945

Subproblem 2

w + 1.5 = -3.640054945 Simplifying w + 1.5 = -3.640054945 Reorder the terms: 1.5 + w = -3.640054945 Solving 1.5 + w = -3.640054945 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -3.640054945 + -1.5 w = -3.640054945 + -1.5 Combine like terms: -3.640054945 + -1.5 = -5.140054945 w = -5.140054945 Simplifying w = -5.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. w = {2.140054945, -5.140054945}

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