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Simplifying 10b2 + 28 = -20b Reorder the terms: 28 + 10b2 = -20b Solving 28 + 10b2 = -20b Solving for variable 'b'. Reorder the terms: 28 + 20b + 10b2 = -20b + 20b Combine like terms: -20b + 20b = 0 28 + 20b + 10b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 10b + 5b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + 10b + 5b2)' equal to zero and attempt to solve: Simplifying 14 + 10b + 5b2 = 0 Solving 14 + 10b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 2b + b2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 2b + -2.8 + b2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 2b + b2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 2b + b2 = 0 + -2.8 2b + b2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 2b + b2 = -2.8 The b term is 2b. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2b + 1 + b2 = -2.8 + 1 Reorder the terms: 1 + 2b + b2 = -2.8 + 1 Combine like terms: -2.8 + 1 = -1.8 1 + 2b + b2 = -1.8 Factor a perfect square on the left side: (b + 1)(b + 1) = -1.8 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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