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Simplifying 2w2 + 4w + 70 = (w + 7)(w + 7) Reorder the terms: 70 + 4w + 2w2 = (w + 7)(w + 7) Reorder the terms: 70 + 4w + 2w2 = (7 + w)(w + 7) Reorder the terms: 70 + 4w + 2w2 = (7 + w)(7 + w) Multiply (7 + w) * (7 + w) 70 + 4w + 2w2 = (7(7 + w) + w(7 + w)) 70 + 4w + 2w2 = ((7 * 7 + w * 7) + w(7 + w)) 70 + 4w + 2w2 = ((49 + 7w) + w(7 + w)) 70 + 4w + 2w2 = (49 + 7w + (7 * w + w * w)) 70 + 4w + 2w2 = (49 + 7w + (7w + w2)) Combine like terms: 7w + 7w = 14w 70 + 4w + 2w2 = (49 + 14w + w2) Solving 70 + 4w + 2w2 = 49 + 14w + w2 Solving for variable 'w'. Reorder the terms: 70 + -49 + 4w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2 Combine like terms: 70 + -49 = 21 21 + 4w + -14w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2 Combine like terms: 4w + -14w = -10w 21 + -10w + 2w2 + -1w2 = 49 + 14w + w2 + -49 + -14w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 21 + -10w + 1w2 = 49 + 14w + w2 + -49 + -14w + -1w2 Reorder the terms: 21 + -10w + 1w2 = 49 + -49 + 14w + -14w + w2 + -1w2 Combine like terms: 49 + -49 = 0 21 + -10w + 1w2 = 0 + 14w + -14w + w2 + -1w2 21 + -10w + 1w2 = 14w + -14w + w2 + -1w2 Combine like terms: 14w + -14w = 0 21 + -10w + 1w2 = 0 + w2 + -1w2 21 + -10w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 21 + -10w + 1w2 = 0 Factor a trinomial. (3 + -1w)(7 + -1w) = 0Subproblem 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 = 3Subproblem 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 = 7Solution
w = {3, 7}
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