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Simplifying -1b2 + -7 = b Reorder the terms: -7 + -1b2 = b Solving -7 + -1b2 = b Solving for variable 'b'. Reorder the terms: -7 + -1b + -1b2 = b + -1b Combine like terms: b + -1b = 0 -7 + -1b + -1b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + b + b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + b + b2)' equal to zero and attempt to solve: Simplifying 7 + b + b2 = 0 Solving 7 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + b + -7 + b2 = 0 + -7 Reorder the terms: 7 + -7 + b + b2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + b + b2 = 0 + -7 b + b2 = 0 + -7 Combine like terms: 0 + -7 = -7 b + b2 = -7 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. b + 0.25 + b2 = -7 + 0.25 Reorder the terms: 0.25 + b + b2 = -7 + 0.25 Combine like terms: -7 + 0.25 = -6.75 0.25 + b + b2 = -6.75 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = -6.75 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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