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Simplifying w2 + -4w + -3 = 0 Reorder the terms: -3 + -4w + w2 = 0 Solving -3 + -4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -4w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + -4w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4w + w2 = 0 + 3 -4w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4w + w2 = 3 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 3 + 4 Reorder the terms: 4 + -4w + w2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4w + w2 = 7 Factor a perfect square on the left side: (w + -2)(w + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (w + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
w + -2 = 2.645751311 Simplifying w + -2 = 2.645751311 Reorder the terms: -2 + w = 2.645751311 Solving -2 + w = 2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + w = 2.645751311 + 2 w = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 w = 4.645751311 Simplifying w = 4.645751311Subproblem 2
w + -2 = -2.645751311 Simplifying w + -2 = -2.645751311 Reorder the terms: -2 + w = -2.645751311 Solving -2 + w = -2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + w = -2.645751311 + 2 w = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 w = -0.645751311 Simplifying w = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.645751311, -0.645751311}
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