w^2=-3w+18

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Solution for w^2=-3w+18 equation:


Simplifying
w2 = -3w + 18

Reorder the terms:
w2 = 18 + -3w

Solving
w2 = 18 + -3w

Solving for variable 'w'.

Reorder the terms:
-18 + 3w + w2 = 18 + -3w + -18 + 3w

Reorder the terms:
-18 + 3w + w2 = 18 + -18 + -3w + 3w

Combine like terms: 18 + -18 = 0
-18 + 3w + w2 = 0 + -3w + 3w
-18 + 3w + w2 = -3w + 3w

Combine like terms: -3w + 3w = 0
-18 + 3w + w2 = 0

Factor a trinomial.
(-6 + -1w)(3 + -1w) = 0

Subproblem 1

Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6

Subproblem 2

Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3

Solution

w = {-6, 3}

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