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Simplifying -8b2 + -5b + -12 = -7 Reorder the terms: -12 + -5b + -8b2 = -7 Solving -12 + -5b + -8b2 = -7 Solving for variable 'b'. Reorder the terms: -12 + 7 + -5b + -8b2 = -7 + 7 Combine like terms: -12 + 7 = -5 -5 + -5b + -8b2 = -7 + 7 Combine like terms: -7 + 7 = 0 -5 + -5b + -8b2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 5b + 8b2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 5b + 8b2)' equal to zero and attempt to solve: Simplifying 5 + 5b + 8b2 = 0 Solving 5 + 5b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 0.625b + b2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 0.625b + -0.625 + b2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 0.625b + b2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 0.625b + b2 = 0 + -0.625 0.625b + b2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 0.625b + b2 = -0.625 The b term is 0.625b. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625b + 0.09765625 + b2 = -0.625 + 0.09765625 Reorder the terms: 0.09765625 + 0.625b + b2 = -0.625 + 0.09765625 Combine like terms: -0.625 + 0.09765625 = -0.52734375 0.09765625 + 0.625b + b2 = -0.52734375 Factor a perfect square on the left side: (b + 0.3125)(b + 0.3125) = -0.52734375 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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