0=w^2+11w+28

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Solution for 0=w^2+11w+28 equation:


Simplifying
0 = w2 + 11w + 28

Reorder the terms:
0 = 28 + 11w + w2

Solving
0 = 28 + 11w + w2

Solving for variable 'w'.

Combine like terms: 0 + -28 = -28
-28 + -11w + -1w2 = 28 + 11w + w2 + -28 + -11w + -1w2

Reorder the terms:
-28 + -11w + -1w2 = 28 + -28 + 11w + -11w + w2 + -1w2

Combine like terms: 28 + -28 = 0
-28 + -11w + -1w2 = 0 + 11w + -11w + w2 + -1w2
-28 + -11w + -1w2 = 11w + -11w + w2 + -1w2

Combine like terms: 11w + -11w = 0
-28 + -11w + -1w2 = 0 + w2 + -1w2
-28 + -11w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-28 + -11w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 11w + w2) = 0

Factor a trinomial.
-1((7 + w)(4 + w)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 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 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7

Subproblem 2

Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4

Solution

w = {-7, -4}

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