(2w-1)(w)=55

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Solution for (2w-1)(w)=55 equation:


Simplifying
(2w + -1)(w) = 55

Reorder the terms:
(-1 + 2w)(w) = 55

Reorder the terms for easier multiplication:
w(-1 + 2w) = 55
(-1 * w + 2w * w) = 55
(-1w + 2w2) = 55

Solving
-1w + 2w2 = 55

Solving for variable 'w'.

Reorder the terms:
-55 + -1w + 2w2 = 55 + -55

Combine like terms: 55 + -55 = 0
-55 + -1w + 2w2 = 0

Factor a trinomial.
(-5 + -1w)(11 + -2w) = 0

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 '(11 + -2w)' equal to zero and attempt to solve: Simplifying 11 + -2w = 0 Solving 11 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2w = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2w = 0 + -11 -2w = 0 + -11 Combine like terms: 0 + -11 = -11 -2w = -11 Divide each side by '-2'. w = 5.5 Simplifying w = 5.5

Solution

w = {-5, 5.5}

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