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Simplifying (8b2 + -5b + 7) * 6b2 = 0 Reorder the terms: (7 + -5b + 8b2) * 6b2 = 0 Reorder the terms for easier multiplication: 6b2(7 + -5b + 8b2) = 0 (7 * 6b2 + -5b * 6b2 + 8b2 * 6b2) = 0 (42b2 + -30b3 + 48b4) = 0 Solving 42b2 + -30b3 + 48b4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '6b2'. 6b2(7 + -5b + 8b2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve: Simplifying b2 = 0 Solving b2 = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b2 = 0 Take the square root of each side: b = {0}Subproblem 2
Set the factor '(7 + -5b + 8b2)' equal to zero and attempt to solve: Simplifying 7 + -5b + 8b2 = 0 Solving 7 + -5b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + -0.625b + b2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -0.625b + -0.875 + b2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -0.625b + b2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -0.625b + b2 = 0 + -0.875 -0.625b + b2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -0.625b + b2 = -0.875 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 = -0.875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625b + b2 = -0.875 + 0.09765625 Combine like terms: -0.875 + 0.09765625 = -0.77734375 0.09765625 + -0.625b + b2 = -0.77734375 Factor a perfect square on the left side: (b + -0.3125)(b + -0.3125) = -0.77734375 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.Solution
b = {0}
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