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Simplifying (2w + -10)(2w + -10) + -5(2w + -10) + 6 = 0 Reorder the terms: (-10 + 2w)(2w + -10) + -5(2w + -10) + 6 = 0 Reorder the terms: (-10 + 2w)(-10 + 2w) + -5(2w + -10) + 6 = 0 Multiply (-10 + 2w) * (-10 + 2w) (-10(-10 + 2w) + 2w * (-10 + 2w)) + -5(2w + -10) + 6 = 0 ((-10 * -10 + 2w * -10) + 2w * (-10 + 2w)) + -5(2w + -10) + 6 = 0 ((100 + -20w) + 2w * (-10 + 2w)) + -5(2w + -10) + 6 = 0 (100 + -20w + (-10 * 2w + 2w * 2w)) + -5(2w + -10) + 6 = 0 (100 + -20w + (-20w + 4w2)) + -5(2w + -10) + 6 = 0 Combine like terms: -20w + -20w = -40w (100 + -40w + 4w2) + -5(2w + -10) + 6 = 0 Reorder the terms: 100 + -40w + 4w2 + -5(-10 + 2w) + 6 = 0 100 + -40w + 4w2 + (-10 * -5 + 2w * -5) + 6 = 0 100 + -40w + 4w2 + (50 + -10w) + 6 = 0 Reorder the terms: 100 + 50 + 6 + -40w + -10w + 4w2 = 0 Combine like terms: 100 + 50 = 150 150 + 6 + -40w + -10w + 4w2 = 0 Combine like terms: 150 + 6 = 156 156 + -40w + -10w + 4w2 = 0 Combine like terms: -40w + -10w = -50w 156 + -50w + 4w2 = 0 Solving 156 + -50w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(78 + -25w + 2w2) = 0 Factor a trinomial. 2((6 + -1w)(13 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Subproblem 2
Set the factor '(13 + -2w)' equal to zero and attempt to solve: Simplifying 13 + -2w = 0 Solving 13 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2w = 0 + -13 -2w = 0 + -13 Combine like terms: 0 + -13 = -13 -2w = -13 Divide each side by '-2'. w = 6.5 Simplifying w = 6.5Solution
w = {6, 6.5}
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