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Simplifying 5b2 + -4b = 0.2 Reorder the terms: -4b + 5b2 = 0.2 Solving -4b + 5b2 = 0.2 Solving for variable 'b'. Reorder the terms: -0.2 + -4b + 5b2 = 0.2 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 -0.2 + -4b + 5b2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.04 + -0.8b + b2 = 0.0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.8b + 0.04 + b2 = 0.0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.8b + b2 = 0.0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.8b + b2 = 0.0 + 0.04 -0.8b + b2 = 0.0 + 0.04 Combine like terms: 0.0 + 0.04 = 0.04 -0.8b + b2 = 0.04 The b term is -0.8b. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8b + 0.16 + b2 = 0.04 + 0.16 Reorder the terms: 0.16 + -0.8b + b2 = 0.04 + 0.16 Combine like terms: 0.04 + 0.16 = 0.2 0.16 + -0.8b + b2 = 0.2 Factor a perfect square on the left side: (b + -0.4)(b + -0.4) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (b + -0.4) equal to 0.447213596 and -0.447213596.Subproblem 1
b + -0.4 = 0.447213596 Simplifying b + -0.4 = 0.447213596 Reorder the terms: -0.4 + b = 0.447213596 Solving -0.4 + b = 0.447213596 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + b = 0.447213596 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + b = 0.447213596 + 0.4 b = 0.447213596 + 0.4 Combine like terms: 0.447213596 + 0.4 = 0.847213596 b = 0.847213596 Simplifying b = 0.847213596Subproblem 2
b + -0.4 = -0.447213596 Simplifying b + -0.4 = -0.447213596 Reorder the terms: -0.4 + b = -0.447213596 Solving -0.4 + b = -0.447213596 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + b = -0.447213596 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + b = -0.447213596 + 0.4 b = -0.447213596 + 0.4 Combine like terms: -0.447213596 + 0.4 = -0.047213596 b = -0.047213596 Simplifying b = -0.047213596Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.847213596, -0.047213596}
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