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Simplifying (6w2 + -5w + -8) + -1(7w2 + 4w + -2) = 0 Reorder the terms: (-8 + -5w + 6w2) + -1(7w2 + 4w + -2) = 0 Remove parenthesis around (-8 + -5w + 6w2) -8 + -5w + 6w2 + -1(7w2 + 4w + -2) = 0 Reorder the terms: -8 + -5w + 6w2 + -1(-2 + 4w + 7w2) = 0 -8 + -5w + 6w2 + (-2 * -1 + 4w * -1 + 7w2 * -1) = 0 -8 + -5w + 6w2 + (2 + -4w + -7w2) = 0 Reorder the terms: -8 + 2 + -5w + -4w + 6w2 + -7w2 = 0 Combine like terms: -8 + 2 = -6 -6 + -5w + -4w + 6w2 + -7w2 = 0 Combine like terms: -5w + -4w = -9w -6 + -9w + 6w2 + -7w2 = 0 Combine like terms: 6w2 + -7w2 = -1w2 -6 + -9w + -1w2 = 0 Solving -6 + -9w + -1w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 9w + w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 9w + w2)' equal to zero and attempt to solve: Simplifying 6 + 9w + w2 = 0 Solving 6 + 9w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 9w + -6 + w2 = 0 + -6 Reorder the terms: 6 + -6 + 9w + w2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 9w + w2 = 0 + -6 9w + w2 = 0 + -6 Combine like terms: 0 + -6 = -6 9w + w2 = -6 The w term is 9w. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9w + 20.25 + w2 = -6 + 20.25 Reorder the terms: 20.25 + 9w + w2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + 9w + w2 = 14.25 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (w + 4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
w + 4.5 = 3.774917218 Simplifying w + 4.5 = 3.774917218 Reorder the terms: 4.5 + w = 3.774917218 Solving 4.5 + w = 3.774917218 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = 3.774917218 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = 3.774917218 + -4.5 w = 3.774917218 + -4.5 Combine like terms: 3.774917218 + -4.5 = -0.725082782 w = -0.725082782 Simplifying w = -0.725082782Subproblem 2
w + 4.5 = -3.774917218 Simplifying w + 4.5 = -3.774917218 Reorder the terms: 4.5 + w = -3.774917218 Solving 4.5 + w = -3.774917218 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = -3.774917218 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = -3.774917218 + -4.5 w = -3.774917218 + -4.5 Combine like terms: -3.774917218 + -4.5 = -8.274917218 w = -8.274917218 Simplifying w = -8.274917218Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.725082782, -8.274917218}Solution
w = {-0.725082782, -8.274917218}
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