(4w^2)+12w+9=49

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Solution for (4w^2)+12w+9=49 equation:


Simplifying
(4w2) + 12w + 9 = 49

Reorder the terms:
9 + 12w + (4w2) = 49

Solving
9 + 12w + (4w2) = 49

Solving for variable 'w'.

Reorder the terms:
9 + -49 + 12w + (4w2) = 49 + -49

Combine like terms: 9 + -49 = -40
-40 + 12w + (4w2) = 49 + -49

Combine like terms: 49 + -49 = 0
-40 + 12w + (4w2) = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 3w + w2) = 0

Factor a trinomial.
4((-5 + -1w)(2 + -1w)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5

Subproblem 2

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

Solution

w = {-5, 2}

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