(w*w)-10=w+2

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Solution for (w*w)-10=w+2 equation:


Simplifying
(w * w) + -10 = w + 2

Multiply w * w
(w2) + -10 = w + 2
w2 + -10 = w + 2

Reorder the terms:
-10 + w2 = w + 2

Reorder the terms:
-10 + w2 = 2 + w

Solving
-10 + w2 = 2 + w

Solving for variable 'w'.

Reorder the terms:
-10 + -2 + -1w + w2 = 2 + w + -2 + -1w

Combine like terms: -10 + -2 = -12
-12 + -1w + w2 = 2 + w + -2 + -1w

Reorder the terms:
-12 + -1w + w2 = 2 + -2 + w + -1w

Combine like terms: 2 + -2 = 0
-12 + -1w + w2 = 0 + w + -1w
-12 + -1w + w2 = w + -1w

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