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Simplifying (-1w2 + 5w + -6) + (3w2 + 7w + 4) = 0 Reorder the terms: (-6 + 5w + -1w2) + (3w2 + 7w + 4) = 0 Remove parenthesis around (-6 + 5w + -1w2) -6 + 5w + -1w2 + (3w2 + 7w + 4) = 0 Reorder the terms: -6 + 5w + -1w2 + (4 + 7w + 3w2) = 0 Remove parenthesis around (4 + 7w + 3w2) -6 + 5w + -1w2 + 4 + 7w + 3w2 = 0 Reorder the terms: -6 + 4 + 5w + 7w + -1w2 + 3w2 = 0 Combine like terms: -6 + 4 = -2 -2 + 5w + 7w + -1w2 + 3w2 = 0 Combine like terms: 5w + 7w = 12w -2 + 12w + -1w2 + 3w2 = 0 Combine like terms: -1w2 + 3w2 = 2w2 -2 + 12w + 2w2 = 0 Solving -2 + 12w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 6w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 6w + w2)' equal to zero and attempt to solve: Simplifying -1 + 6w + w2 = 0 Solving -1 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 6w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + 6w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6w + w2 = 0 + 1 6w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 6w + w2 = 1 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 1 + 9 Reorder the terms: 9 + 6w + w2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + 6w + w2 = 10 Factor a perfect square on the left side: (w + 3)(w + 3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (w + 3) equal to 3.16227766 and -3.16227766.Subproblem 1
w + 3 = 3.16227766 Simplifying w + 3 = 3.16227766 Reorder the terms: 3 + w = 3.16227766 Solving 3 + w = 3.16227766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + w = 3.16227766 + -3 w = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 w = 0.16227766 Simplifying w = 0.16227766Subproblem 2
w + 3 = -3.16227766 Simplifying w + 3 = -3.16227766 Reorder the terms: 3 + w = -3.16227766 Solving 3 + w = -3.16227766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + w = -3.16227766 + -3 w = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 w = -6.16227766 Simplifying w = -6.16227766Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.16227766, -6.16227766}Solution
w = {0.16227766, -6.16227766}
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