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Simplifying 3W2 + 4W + 11 = 2 + -2W Reorder the terms: 11 + 4W + 3W2 = 2 + -2W Solving 11 + 4W + 3W2 = 2 + -2W Solving for variable 'W'. Reorder the terms: 11 + -2 + 4W + 2W + 3W2 = 2 + -2W + -2 + 2W Combine like terms: 11 + -2 = 9 9 + 4W + 2W + 3W2 = 2 + -2W + -2 + 2W Combine like terms: 4W + 2W = 6W 9 + 6W + 3W2 = 2 + -2W + -2 + 2W Reorder the terms: 9 + 6W + 3W2 = 2 + -2 + -2W + 2W Combine like terms: 2 + -2 = 0 9 + 6W + 3W2 = 0 + -2W + 2W 9 + 6W + 3W2 = -2W + 2W Combine like terms: -2W + 2W = 0 9 + 6W + 3W2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 2W + W2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 2W + W2)' equal to zero and attempt to solve: Simplifying 3 + 2W + W2 = 0 Solving 3 + 2W + W2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2W + -3 + W2 = 0 + -3 Reorder the terms: 3 + -3 + 2W + W2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2W + W2 = 0 + -3 2W + W2 = 0 + -3 Combine like terms: 0 + -3 = -3 2W + W2 = -3 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 = -3 + 1 Reorder the terms: 1 + 2W + W2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + 2W + W2 = -2 Factor a perfect square on the left side: (W + 1)(W + 1) = -2 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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