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Simplifying 4w2 = 12w + 7 Reorder the terms: 4w2 = 7 + 12w Solving 4w2 = 7 + 12w Solving for variable 'w'. Reorder the terms: -7 + -12w + 4w2 = 7 + 12w + -7 + -12w Reorder the terms: -7 + -12w + 4w2 = 7 + -7 + 12w + -12w Combine like terms: 7 + -7 = 0 -7 + -12w + 4w2 = 0 + 12w + -12w -7 + -12w + 4w2 = 12w + -12w Combine like terms: 12w + -12w = 0 -7 + -12w + 4w2 = 0 Factor a trinomial. (-1 + -2w)(7 + -2w) = 0Subproblem 1
Set the factor '(-1 + -2w)' equal to zero and attempt to solve: Simplifying -1 + -2w = 0 Solving -1 + -2w = 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 + -2w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2w = 0 + 1 -2w = 0 + 1 Combine like terms: 0 + 1 = 1 -2w = 1 Divide each side by '-2'. w = -0.5 Simplifying w = -0.5Subproblem 2
Set the factor '(7 + -2w)' equal to zero and attempt to solve: Simplifying 7 + -2w = 0 Solving 7 + -2w = 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 + -2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2w = 0 + -7 -2w = 0 + -7 Combine like terms: 0 + -7 = -7 -2w = -7 Divide each side by '-2'. w = 3.5 Simplifying w = 3.5Solution
w = {-0.5, 3.5}
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