2w^2+9w+53=w^2+14w+49

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Solution for 2w^2+9w+53=w^2+14w+49 equation:


Simplifying
2w2 + 9w + 53 = w2 + 14w + 49

Reorder the terms:
53 + 9w + 2w2 = w2 + 14w + 49

Reorder the terms:
53 + 9w + 2w2 = 49 + 14w + w2

Solving
53 + 9w + 2w2 = 49 + 14w + w2

Solving for variable 'w'.

Reorder the terms:
53 + -49 + 9w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 53 + -49 = 4
4 + 9w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 9w + -14w = -5w
4 + -5w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
4 + -5w + 1w2 = 49 + 14w + w2 + -49 + -14w + -1w2

Reorder the terms:
4 + -5w + 1w2 = 49 + -49 + 14w + -14w + w2 + -1w2

Combine like terms: 49 + -49 = 0
4 + -5w + 1w2 = 0 + 14w + -14w + w2 + -1w2
4 + -5w + 1w2 = 14w + -14w + w2 + -1w2

Combine like terms: 14w + -14w = 0
4 + -5w + 1w2 = 0 + w2 + -1w2
4 + -5w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
4 + -5w + 1w2 = 0

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

Subproblem 1

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

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 = {1, 4}

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