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Simplifying 25b2 + 4b + -4 = 0 Reorder the terms: -4 + 4b + 25b2 = 0 Solving -4 + 4b + 25b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + 0.16b + b2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + 0.16b + 0.16 + b2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + 0.16b + b2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + 0.16b + b2 = 0 + 0.16 0.16b + b2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 0.16b + b2 = 0.16 The b term is 0.16b. Take half its coefficient (0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. 0.16b + 0.0064 + b2 = 0.16 + 0.0064 Reorder the terms: 0.0064 + 0.16b + b2 = 0.16 + 0.0064 Combine like terms: 0.16 + 0.0064 = 0.1664 0.0064 + 0.16b + b2 = 0.1664 Factor a perfect square on the left side: (b + 0.08)(b + 0.08) = 0.1664 Calculate the square root of the right side: 0.407921561 Break this problem into two subproblems by setting (b + 0.08) equal to 0.407921561 and -0.407921561.Subproblem 1
b + 0.08 = 0.407921561 Simplifying b + 0.08 = 0.407921561 Reorder the terms: 0.08 + b = 0.407921561 Solving 0.08 + b = 0.407921561 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + b = 0.407921561 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + b = 0.407921561 + -0.08 b = 0.407921561 + -0.08 Combine like terms: 0.407921561 + -0.08 = 0.327921561 b = 0.327921561 Simplifying b = 0.327921561Subproblem 2
b + 0.08 = -0.407921561 Simplifying b + 0.08 = -0.407921561 Reorder the terms: 0.08 + b = -0.407921561 Solving 0.08 + b = -0.407921561 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + b = -0.407921561 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + b = -0.407921561 + -0.08 b = -0.407921561 + -0.08 Combine like terms: -0.407921561 + -0.08 = -0.487921561 b = -0.487921561 Simplifying b = -0.487921561Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.327921561, -0.487921561}
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