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Simplifying b2 + 4b + -37 = 10 Reorder the terms: -37 + 4b + b2 = 10 Solving -37 + 4b + b2 = 10 Solving for variable 'b'. Reorder the terms: -37 + -10 + 4b + b2 = 10 + -10 Combine like terms: -37 + -10 = -47 -47 + 4b + b2 = 10 + -10 Combine like terms: 10 + -10 = 0 -47 + 4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 4b + 47 + b2 = 0 + 47 Reorder the terms: -47 + 47 + 4b + b2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 4b + b2 = 0 + 47 4b + b2 = 0 + 47 Combine like terms: 0 + 47 = 47 4b + b2 = 47 The b term is 4b. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4b + 4 + b2 = 47 + 4 Reorder the terms: 4 + 4b + b2 = 47 + 4 Combine like terms: 47 + 4 = 51 4 + 4b + b2 = 51 Factor a perfect square on the left side: (b + 2)(b + 2) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (b + 2) equal to 7.141428429 and -7.141428429.Subproblem 1
b + 2 = 7.141428429 Simplifying b + 2 = 7.141428429 Reorder the terms: 2 + b = 7.141428429 Solving 2 + b = 7.141428429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = 7.141428429 + -2 Combine like terms: 2 + -2 = 0 0 + b = 7.141428429 + -2 b = 7.141428429 + -2 Combine like terms: 7.141428429 + -2 = 5.141428429 b = 5.141428429 Simplifying b = 5.141428429Subproblem 2
b + 2 = -7.141428429 Simplifying b + 2 = -7.141428429 Reorder the terms: 2 + b = -7.141428429 Solving 2 + b = -7.141428429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = -7.141428429 + -2 Combine like terms: 2 + -2 = 0 0 + b = -7.141428429 + -2 b = -7.141428429 + -2 Combine like terms: -7.141428429 + -2 = -9.141428429 b = -9.141428429 Simplifying b = -9.141428429Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.141428429, -9.141428429}
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