4w^2+20w+9=0

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Solution for 4w^2+20w+9=0 equation:


Simplifying
4w2 + 20w + 9 = 0

Reorder the terms:
9 + 20w + 4w2 = 0

Solving
9 + 20w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + 2w)(1 + 2w) = 0

Subproblem 1

Set the factor '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5

Subproblem 2

Set the factor '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5

Solution

w = {-4.5, -0.5}

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