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Simplifying w2 + 10w + 25 = 2w2 + 4w + 30 Reorder the terms: 25 + 10w + w2 = 2w2 + 4w + 30 Reorder the terms: 25 + 10w + w2 = 30 + 4w + 2w2 Solving 25 + 10w + w2 = 30 + 4w + 2w2 Solving for variable 'w'. Reorder the terms: 25 + -30 + 10w + -4w + w2 + -2w2 = 30 + 4w + 2w2 + -30 + -4w + -2w2 Combine like terms: 25 + -30 = -5 -5 + 10w + -4w + w2 + -2w2 = 30 + 4w + 2w2 + -30 + -4w + -2w2 Combine like terms: 10w + -4w = 6w -5 + 6w + w2 + -2w2 = 30 + 4w + 2w2 + -30 + -4w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -5 + 6w + -1w2 = 30 + 4w + 2w2 + -30 + -4w + -2w2 Reorder the terms: -5 + 6w + -1w2 = 30 + -30 + 4w + -4w + 2w2 + -2w2 Combine like terms: 30 + -30 = 0 -5 + 6w + -1w2 = 0 + 4w + -4w + 2w2 + -2w2 -5 + 6w + -1w2 = 4w + -4w + 2w2 + -2w2 Combine like terms: 4w + -4w = 0 -5 + 6w + -1w2 = 0 + 2w2 + -2w2 -5 + 6w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -5 + 6w + -1w2 = 0 Factor a trinomial. (-5 + w)(1 + -1w) = 0Subproblem 1
Set the factor '(-5 + w)' equal to zero and attempt to solve: Simplifying -5 + w = 0 Solving -5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w = 0 + 5 w = 0 + 5 Combine like terms: 0 + 5 = 5 w = 5 Simplifying w = 5Subproblem 2
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 = 1Solution
w = {5, 1}
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