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Simplifying 2b2 + b + -25 = 0 Reorder the terms: -25 + b + 2b2 = 0 Solving -25 + b + 2b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 0.5b + b2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 0.5b + 12.5 + b2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 0.5b + b2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 0.5b + b2 = 0 + 12.5 0.5b + b2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 0.5b + b2 = 12.5 The b term is b. 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. 0.5b + 0.25 + b2 = 12.5 + 0.25 Reorder the terms: 0.25 + 0.5b + b2 = 12.5 + 0.25 Combine like terms: 12.5 + 0.25 = 12.75 0.25 + 0.5b + b2 = 12.75 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (b + 0.5) equal to 3.570714214 and -3.570714214.Subproblem 1
b + 0.5 = 3.570714214 Simplifying b + 0.5 = 3.570714214 Reorder the terms: 0.5 + b = 3.570714214 Solving 0.5 + b = 3.570714214 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 = 3.570714214 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 3.570714214 + -0.5 b = 3.570714214 + -0.5 Combine like terms: 3.570714214 + -0.5 = 3.070714214 b = 3.070714214 Simplifying b = 3.070714214Subproblem 2
b + 0.5 = -3.570714214 Simplifying b + 0.5 = -3.570714214 Reorder the terms: 0.5 + b = -3.570714214 Solving 0.5 + b = -3.570714214 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 = -3.570714214 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -3.570714214 + -0.5 b = -3.570714214 + -0.5 Combine like terms: -3.570714214 + -0.5 = -4.070714214 b = -4.070714214 Simplifying b = -4.070714214Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.070714214, -4.070714214}
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