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Simplifying 5b2 + 5b + 450 = 0 Reorder the terms: 450 + 5b + 5b2 = 0 Solving 450 + 5b + 5b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5'. 5(90 + b + b2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(90 + b + b2)' equal to zero and attempt to solve: Simplifying 90 + b + b2 = 0 Solving 90 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + b + -90 + b2 = 0 + -90 Reorder the terms: 90 + -90 + b + b2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + b + b2 = 0 + -90 b + b2 = 0 + -90 Combine like terms: 0 + -90 = -90 b + b2 = -90 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 = -90 + 0.25 Reorder the terms: 0.25 + b + b2 = -90 + 0.25 Combine like terms: -90 + 0.25 = -89.75 0.25 + b + b2 = -89.75 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = -89.75 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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