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Simplifying 3(w2 + -10w + 25) = 45 Reorder the terms: 3(25 + -10w + w2) = 45 (25 * 3 + -10w * 3 + w2 * 3) = 45 (75 + -30w + 3w2) = 45 Solving 75 + -30w + 3w2 = 45 Solving for variable 'w'. Reorder the terms: 75 + -45 + -30w + 3w2 = 45 + -45 Combine like terms: 75 + -45 = 30 30 + -30w + 3w2 = 45 + -45 Combine like terms: 45 + -45 = 0 30 + -30w + 3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -10w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -10w + w2)' equal to zero and attempt to solve: Simplifying 10 + -10w + w2 = 0 Solving 10 + -10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10w + -10 + w2 = 0 + -10 Reorder the terms: 10 + -10 + -10w + w2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10w + w2 = 0 + -10 -10w + w2 = 0 + -10 Combine like terms: 0 + -10 = -10 -10w + w2 = -10 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 = -10 + 25 Reorder the terms: 25 + -10w + w2 = -10 + 25 Combine like terms: -10 + 25 = 15 25 + -10w + w2 = 15 Factor a perfect square on the left side: (w + -5)(w + -5) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (w + -5) equal to 3.872983346 and -3.872983346.Subproblem 1
w + -5 = 3.872983346 Simplifying w + -5 = 3.872983346 Reorder the terms: -5 + w = 3.872983346 Solving -5 + w = 3.872983346 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 = 3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + w = 3.872983346 + 5 w = 3.872983346 + 5 Combine like terms: 3.872983346 + 5 = 8.872983346 w = 8.872983346 Simplifying w = 8.872983346Subproblem 2
w + -5 = -3.872983346 Simplifying w + -5 = -3.872983346 Reorder the terms: -5 + w = -3.872983346 Solving -5 + w = -3.872983346 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 = -3.872983346 + 5 Combine like terms: -5 + 5 = 0 0 + w = -3.872983346 + 5 w = -3.872983346 + 5 Combine like terms: -3.872983346 + 5 = 1.127016654 w = 1.127016654 Simplifying w = 1.127016654Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.872983346, 1.127016654}Solution
w = {8.872983346, 1.127016654}
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