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Simplifying 6w2 + -1 = 25(w + 2) Reorder the terms: -1 + 6w2 = 25(w + 2) Reorder the terms: -1 + 6w2 = 25(2 + w) -1 + 6w2 = (2 * 25 + w * 25) -1 + 6w2 = (50 + 25w) Solving -1 + 6w2 = 50 + 25w Solving for variable 'w'. Reorder the terms: -1 + -50 + -25w + 6w2 = 50 + 25w + -50 + -25w Combine like terms: -1 + -50 = -51 -51 + -25w + 6w2 = 50 + 25w + -50 + -25w Reorder the terms: -51 + -25w + 6w2 = 50 + -50 + 25w + -25w Combine like terms: 50 + -50 = 0 -51 + -25w + 6w2 = 0 + 25w + -25w -51 + -25w + 6w2 = 25w + -25w Combine like terms: 25w + -25w = 0 -51 + -25w + 6w2 = 0 Factor a trinomial. (-3 + -2w)(17 + -3w) = 0Subproblem 1
Set the factor '(-3 + -2w)' equal to zero and attempt to solve: Simplifying -3 + -2w = 0 Solving -3 + -2w = 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 + -2w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2w = 0 + 3 -2w = 0 + 3 Combine like terms: 0 + 3 = 3 -2w = 3 Divide each side by '-2'. w = -1.5 Simplifying w = -1.5Subproblem 2
Set the factor '(17 + -3w)' equal to zero and attempt to solve: Simplifying 17 + -3w = 0 Solving 17 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -3w = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3w = 0 + -17 -3w = 0 + -17 Combine like terms: 0 + -17 = -17 -3w = -17 Divide each side by '-3'. w = 5.666666667 Simplifying w = 5.666666667Solution
w = {-1.5, 5.666666667}
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