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Simplifying 0 = w2 + 6w + 150 Reorder the terms: 0 = 150 + 6w + w2 Solving 0 = 150 + 6w + w2 Solving for variable 'w'. Combine like terms: 0 + -150 = -150 -150 + -6w + -1w2 = 150 + 6w + w2 + -150 + -6w + -1w2 Reorder the terms: -150 + -6w + -1w2 = 150 + -150 + 6w + -6w + w2 + -1w2 Combine like terms: 150 + -150 = 0 -150 + -6w + -1w2 = 0 + 6w + -6w + w2 + -1w2 -150 + -6w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 -150 + -6w + -1w2 = 0 + w2 + -1w2 -150 + -6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -150 + -6w + -1w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(150 + 6w + w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(150 + 6w + w2)' equal to zero and attempt to solve: Simplifying 150 + 6w + w2 = 0 Solving 150 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + 6w + -150 + w2 = 0 + -150 Reorder the terms: 150 + -150 + 6w + w2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + 6w + w2 = 0 + -150 6w + w2 = 0 + -150 Combine like terms: 0 + -150 = -150 6w + w2 = -150 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 = -150 + 9 Reorder the terms: 9 + 6w + w2 = -150 + 9 Combine like terms: -150 + 9 = -141 9 + 6w + w2 = -141 Factor a perfect square on the left side: (w + 3)(w + 3) = -141 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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