w^2+4w=77

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Solution for w^2+4w=77 equation:


Simplifying
w2 + 4w = 77

Reorder the terms:
4w + w2 = 77

Solving
4w + w2 = 77

Solving for variable 'w'.

Reorder the terms:
-77 + 4w + w2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 4w + w2 = 0

Factor a trinomial.
(-11 + -1w)(7 + -1w) = 0

Subproblem 1

Set the factor '(-11 + -1w)' equal to zero and attempt to solve: Simplifying -11 + -1w = 0 Solving -11 + -1w = 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 + -1w = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1w = 0 + 11 -1w = 0 + 11 Combine like terms: 0 + 11 = 11 -1w = 11 Divide each side by '-1'. w = -11 Simplifying w = -11

Subproblem 2

Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7

Solution

w = {-11, 7}

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