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Simplifying 5b2 + -5b = 6 Reorder the terms: -5b + 5b2 = 6 Solving -5b + 5b2 = 6 Solving for variable 'b'. Reorder the terms: -6 + -5b + 5b2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -5b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -1b + b2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1b + 1.2 + b2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1b + b2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1b + b2 = 0 + 1.2 -1b + b2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1b + b2 = 1.2 The b term is -1b. 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. -1b + 0.25 + b2 = 1.2 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 1.2 + 0.25 Combine like terms: 1.2 + 0.25 = 1.45 0.25 + -1b + b2 = 1.45 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (b + -0.5) equal to 1.204159458 and -1.204159458.Subproblem 1
b + -0.5 = 1.204159458 Simplifying b + -0.5 = 1.204159458 Reorder the terms: -0.5 + b = 1.204159458 Solving -0.5 + b = 1.204159458 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 1.204159458 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 1.204159458 + 0.5 b = 1.204159458 + 0.5 Combine like terms: 1.204159458 + 0.5 = 1.704159458 b = 1.704159458 Simplifying b = 1.704159458Subproblem 2
b + -0.5 = -1.204159458 Simplifying b + -0.5 = -1.204159458 Reorder the terms: -0.5 + b = -1.204159458 Solving -0.5 + b = -1.204159458 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -1.204159458 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -1.204159458 + 0.5 b = -1.204159458 + 0.5 Combine like terms: -1.204159458 + 0.5 = -0.704159458 b = -0.704159458 Simplifying b = -0.704159458Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.704159458, -0.704159458}
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