4w^2=44w-72

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Solution for 4w^2=44w-72 equation:


Simplifying
4w2 = 44w + -72

Reorder the terms:
4w2 = -72 + 44w

Solving
4w2 = -72 + 44w

Solving for variable 'w'.

Reorder the terms:
72 + -44w + 4w2 = -72 + 44w + 72 + -44w

Reorder the terms:
72 + -44w + 4w2 = -72 + 72 + 44w + -44w

Combine like terms: -72 + 72 = 0
72 + -44w + 4w2 = 0 + 44w + -44w
72 + -44w + 4w2 = 44w + -44w

Combine like terms: 44w + -44w = 0
72 + -44w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -11w + w2) = 0

Factor a trinomial.
4((2 + -1w)(9 + -1w)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 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 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9

Solution

w = {2, 9}

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