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Simplifying 3(w + -4)(w + -4) = 34 Reorder the terms: 3(-4 + w)(w + -4) = 34 Reorder the terms: 3(-4 + w)(-4 + w) = 34 Multiply (-4 + w) * (-4 + w) 3(-4(-4 + w) + w(-4 + w)) = 34 3((-4 * -4 + w * -4) + w(-4 + w)) = 34 3((16 + -4w) + w(-4 + w)) = 34 3(16 + -4w + (-4 * w + w * w)) = 34 3(16 + -4w + (-4w + w2)) = 34 Combine like terms: -4w + -4w = -8w 3(16 + -8w + w2) = 34 (16 * 3 + -8w * 3 + w2 * 3) = 34 (48 + -24w + 3w2) = 34 Solving 48 + -24w + 3w2 = 34 Solving for variable 'w'. Reorder the terms: 48 + -34 + -24w + 3w2 = 34 + -34 Combine like terms: 48 + -34 = 14 14 + -24w + 3w2 = 34 + -34 Combine like terms: 34 + -34 = 0 14 + -24w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.666666667 + -8w + w2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + -8w + -4.666666667 + w2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + -8w + w2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + -8w + w2 = 0 + -4.666666667 -8w + w2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 -8w + w2 = -4.666666667 The w term is -8w. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8w + 16 + w2 = -4.666666667 + 16 Reorder the terms: 16 + -8w + w2 = -4.666666667 + 16 Combine like terms: -4.666666667 + 16 = 11.333333333 16 + -8w + w2 = 11.333333333 Factor a perfect square on the left side: (w + -4)(w + -4) = 11.333333333 Calculate the square root of the right side: 3.366501646 Break this problem into two subproblems by setting (w + -4) equal to 3.366501646 and -3.366501646.Subproblem 1
w + -4 = 3.366501646 Simplifying w + -4 = 3.366501646 Reorder the terms: -4 + w = 3.366501646 Solving -4 + w = 3.366501646 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 3.366501646 + 4 Combine like terms: -4 + 4 = 0 0 + w = 3.366501646 + 4 w = 3.366501646 + 4 Combine like terms: 3.366501646 + 4 = 7.366501646 w = 7.366501646 Simplifying w = 7.366501646Subproblem 2
w + -4 = -3.366501646 Simplifying w + -4 = -3.366501646 Reorder the terms: -4 + w = -3.366501646 Solving -4 + w = -3.366501646 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -3.366501646 + 4 Combine like terms: -4 + 4 = 0 0 + w = -3.366501646 + 4 w = -3.366501646 + 4 Combine like terms: -3.366501646 + 4 = 0.633498354 w = 0.633498354 Simplifying w = 0.633498354Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.366501646, 0.633498354}
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