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Simplifying 2w2 + -16w = -10 Reorder the terms: -16w + 2w2 = -10 Solving -16w + 2w2 = -10 Solving for variable 'w'. Reorder the terms: 10 + -16w + 2w2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -16w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -8w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -8w + w2)' equal to zero and attempt to solve: Simplifying 5 + -8w + w2 = 0 Solving 5 + -8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8w + -5 + w2 = 0 + -5 Reorder the terms: 5 + -5 + -8w + w2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8w + w2 = 0 + -5 -8w + w2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8w + w2 = -5 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 = -5 + 16 Reorder the terms: 16 + -8w + w2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8w + w2 = 11 Factor a perfect square on the left side: (w + -4)(w + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (w + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
w + -4 = 3.31662479 Simplifying w + -4 = 3.31662479 Reorder the terms: -4 + w = 3.31662479 Solving -4 + w = 3.31662479 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 = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + w = 3.31662479 + 4 w = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 w = 7.31662479 Simplifying w = 7.31662479Subproblem 2
w + -4 = -3.31662479 Simplifying w + -4 = -3.31662479 Reorder the terms: -4 + w = -3.31662479 Solving -4 + w = -3.31662479 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 = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + w = -3.31662479 + 4 w = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 w = 0.68337521 Simplifying w = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.31662479, 0.68337521}Solution
w = {7.31662479, 0.68337521}
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