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Simplifying (w + 3)(w + -3) = 10w Reorder the terms: (3 + w)(w + -3) = 10w Reorder the terms: (3 + w)(-3 + w) = 10w Multiply (3 + w) * (-3 + w) (3(-3 + w) + w(-3 + w)) = 10w ((-3 * 3 + w * 3) + w(-3 + w)) = 10w ((-9 + 3w) + w(-3 + w)) = 10w (-9 + 3w + (-3 * w + w * w)) = 10w (-9 + 3w + (-3w + w2)) = 10w Combine like terms: 3w + -3w = 0 (-9 + 0 + w2) = 10w (-9 + w2) = 10w Solving -9 + w2 = 10w Solving for variable 'w'. Reorder the terms: -9 + -10w + w2 = 10w + -10w Combine like terms: 10w + -10w = 0 -9 + -10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -10w + 9 + w2 = 0 + 9 Reorder the terms: -9 + 9 + -10w + w2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -10w + w2 = 0 + 9 -10w + w2 = 0 + 9 Combine like terms: 0 + 9 = 9 -10w + w2 = 9 The w term is -10w. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10w + 25 + w2 = 9 + 25 Reorder the terms: 25 + -10w + w2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + -10w + w2 = 34 Factor a perfect square on the left side: (w + -5)(w + -5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (w + -5) equal to 5.830951895 and -5.830951895.Subproblem 1
w + -5 = 5.830951895 Simplifying w + -5 = 5.830951895 Reorder the terms: -5 + w = 5.830951895 Solving -5 + w = 5.830951895 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + w = 5.830951895 + 5 w = 5.830951895 + 5 Combine like terms: 5.830951895 + 5 = 10.830951895 w = 10.830951895 Simplifying w = 10.830951895Subproblem 2
w + -5 = -5.830951895 Simplifying w + -5 = -5.830951895 Reorder the terms: -5 + w = -5.830951895 Solving -5 + w = -5.830951895 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = -5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + w = -5.830951895 + 5 w = -5.830951895 + 5 Combine like terms: -5.830951895 + 5 = -0.830951895 w = -0.830951895 Simplifying w = -0.830951895Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.830951895, -0.830951895}
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