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Simplifying w2 + -10w + 25 = 2w2 + -21w + 53 Reorder the terms: 25 + -10w + w2 = 2w2 + -21w + 53 Reorder the terms: 25 + -10w + w2 = 53 + -21w + 2w2 Solving 25 + -10w + w2 = 53 + -21w + 2w2 Solving for variable 'w'. Reorder the terms: 25 + -53 + -10w + 21w + w2 + -2w2 = 53 + -21w + 2w2 + -53 + 21w + -2w2 Combine like terms: 25 + -53 = -28 -28 + -10w + 21w + w2 + -2w2 = 53 + -21w + 2w2 + -53 + 21w + -2w2 Combine like terms: -10w + 21w = 11w -28 + 11w + w2 + -2w2 = 53 + -21w + 2w2 + -53 + 21w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -28 + 11w + -1w2 = 53 + -21w + 2w2 + -53 + 21w + -2w2 Reorder the terms: -28 + 11w + -1w2 = 53 + -53 + -21w + 21w + 2w2 + -2w2 Combine like terms: 53 + -53 = 0 -28 + 11w + -1w2 = 0 + -21w + 21w + 2w2 + -2w2 -28 + 11w + -1w2 = -21w + 21w + 2w2 + -2w2 Combine like terms: -21w + 21w = 0 -28 + 11w + -1w2 = 0 + 2w2 + -2w2 -28 + 11w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -28 + 11w + -1w2 = 0 Factor a trinomial. (-7 + w)(4 + -1w) = 0Subproblem 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 = 7Subproblem 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 = 4Solution
w = {7, 4}
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