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Simplifying -1w + -3w + -7 = -2w2 + 3 Reorder the terms: -7 + -1w + -3w = -2w2 + 3 Combine like terms: -1w + -3w = -4w -7 + -4w = -2w2 + 3 Reorder the terms: -7 + -4w = 3 + -2w2 Solving -7 + -4w = 3 + -2w2 Solving for variable 'w'. Reorder the terms: -7 + -3 + -4w + 2w2 = 3 + -2w2 + -3 + 2w2 Combine like terms: -7 + -3 = -10 -10 + -4w + 2w2 = 3 + -2w2 + -3 + 2w2 Reorder the terms: -10 + -4w + 2w2 = 3 + -3 + -2w2 + 2w2 Combine like terms: 3 + -3 = 0 -10 + -4w + 2w2 = 0 + -2w2 + 2w2 -10 + -4w + 2w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 -10 + -4w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -2w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2w + w2)' equal to zero and attempt to solve: Simplifying -5 + -2w + w2 = 0 Solving -5 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2w + 5 + w2 = 0 + 5 Reorder the terms: -5 + 5 + -2w + w2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2w + w2 = 0 + 5 -2w + w2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2w + w2 = 5 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 5 + 1 Reorder the terms: 1 + -2w + w2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2w + w2 = 6 Factor a perfect square on the left side: (w + -1)(w + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (w + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
w + -1 = 2.449489743 Simplifying w + -1 = 2.449489743 Reorder the terms: -1 + w = 2.449489743 Solving -1 + w = 2.449489743 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + w = 2.449489743 + 1 w = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 w = 3.449489743 Simplifying w = 3.449489743Subproblem 2
w + -1 = -2.449489743 Simplifying w + -1 = -2.449489743 Reorder the terms: -1 + w = -2.449489743 Solving -1 + w = -2.449489743 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + w = -2.449489743 + 1 w = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 w = -1.449489743 Simplifying w = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.449489743, -1.449489743}Solution
w = {3.449489743, -1.449489743}
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