(w-3)(w-3)=2w^2-17w+39

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Solution for (w-3)(w-3)=2w^2-17w+39 equation:


Simplifying
(w + -3)(w + -3) = 2w2 + -17w + 39

Reorder the terms:
(-3 + w)(w + -3) = 2w2 + -17w + 39

Reorder the terms:
(-3 + w)(-3 + w) = 2w2 + -17w + 39

Multiply (-3 + w) * (-3 + w)
(-3(-3 + w) + w(-3 + w)) = 2w2 + -17w + 39
((-3 * -3 + w * -3) + w(-3 + w)) = 2w2 + -17w + 39
((9 + -3w) + w(-3 + w)) = 2w2 + -17w + 39
(9 + -3w + (-3 * w + w * w)) = 2w2 + -17w + 39
(9 + -3w + (-3w + w2)) = 2w2 + -17w + 39

Combine like terms: -3w + -3w = -6w
(9 + -6w + w2) = 2w2 + -17w + 39

Reorder the terms:
9 + -6w + w2 = 39 + -17w + 2w2

Solving
9 + -6w + w2 = 39 + -17w + 2w2

Solving for variable 'w'.

Reorder the terms:
9 + -39 + -6w + 17w + w2 + -2w2 = 39 + -17w + 2w2 + -39 + 17w + -2w2

Combine like terms: 9 + -39 = -30
-30 + -6w + 17w + w2 + -2w2 = 39 + -17w + 2w2 + -39 + 17w + -2w2

Combine like terms: -6w + 17w = 11w
-30 + 11w + w2 + -2w2 = 39 + -17w + 2w2 + -39 + 17w + -2w2

Combine like terms: w2 + -2w2 = -1w2
-30 + 11w + -1w2 = 39 + -17w + 2w2 + -39 + 17w + -2w2

Reorder the terms:
-30 + 11w + -1w2 = 39 + -39 + -17w + 17w + 2w2 + -2w2

Combine like terms: 39 + -39 = 0
-30 + 11w + -1w2 = 0 + -17w + 17w + 2w2 + -2w2
-30 + 11w + -1w2 = -17w + 17w + 2w2 + -2w2

Combine like terms: -17w + 17w = 0
-30 + 11w + -1w2 = 0 + 2w2 + -2w2
-30 + 11w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-30 + 11w + -1w2 = 0

Factor a trinomial.
(-6 + w)(5 + -1w) = 0

Subproblem 1

Set the factor '(-6 + w)' equal to zero and attempt to solve: Simplifying -6 + w = 0 Solving -6 + w = 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 + w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + w = 0 + 6 w = 0 + 6 Combine like terms: 0 + 6 = 6 w = 6 Simplifying w = 6

Subproblem 2

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

Solution

w = {6, 5}

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