2w^2-21w+61=w^2-14w+49

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Solution for 2w^2-21w+61=w^2-14w+49 equation:


Simplifying
2w2 + -21w + 61 = w2 + -14w + 49

Reorder the terms:
61 + -21w + 2w2 = w2 + -14w + 49

Reorder the terms:
61 + -21w + 2w2 = 49 + -14w + w2

Solving
61 + -21w + 2w2 = 49 + -14w + w2

Solving for variable 'w'.

Reorder the terms:
61 + -49 + -21w + 14w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2

Combine like terms: 61 + -49 = 12
12 + -21w + 14w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2

Combine like terms: -21w + 14w = -7w
12 + -7w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
12 + -7w + 1w2 = 49 + -14w + w2 + -49 + 14w + -1w2

Reorder the terms:
12 + -7w + 1w2 = 49 + -49 + -14w + 14w + w2 + -1w2

Combine like terms: 49 + -49 = 0
12 + -7w + 1w2 = 0 + -14w + 14w + w2 + -1w2
12 + -7w + 1w2 = -14w + 14w + w2 + -1w2

Combine like terms: -14w + 14w = 0
12 + -7w + 1w2 = 0 + w2 + -1w2
12 + -7w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
12 + -7w + 1w2 = 0

Factor a trinomial.
(3 + -1w)(4 + -1w) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4

Solution

w = {3, 4}

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