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Simplifying b2 + -8b + -58 = 0 Reorder the terms: -58 + -8b + b2 = 0 Solving -58 + -8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -8b + 58 + b2 = 0 + 58 Reorder the terms: -58 + 58 + -8b + b2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -8b + b2 = 0 + 58 -8b + b2 = 0 + 58 Combine like terms: 0 + 58 = 58 -8b + b2 = 58 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = 58 + 16 Reorder the terms: 16 + -8b + b2 = 58 + 16 Combine like terms: 58 + 16 = 74 16 + -8b + b2 = 74 Factor a perfect square on the left side: (b + -4)(b + -4) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (b + -4) equal to 8.602325267 and -8.602325267.Subproblem 1
b + -4 = 8.602325267 Simplifying b + -4 = 8.602325267 Reorder the terms: -4 + b = 8.602325267 Solving -4 + b = 8.602325267 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 8.602325267 + 4 Combine like terms: -4 + 4 = 0 0 + b = 8.602325267 + 4 b = 8.602325267 + 4 Combine like terms: 8.602325267 + 4 = 12.602325267 b = 12.602325267 Simplifying b = 12.602325267Subproblem 2
b + -4 = -8.602325267 Simplifying b + -4 = -8.602325267 Reorder the terms: -4 + b = -8.602325267 Solving -4 + b = -8.602325267 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -8.602325267 + 4 Combine like terms: -4 + 4 = 0 0 + b = -8.602325267 + 4 b = -8.602325267 + 4 Combine like terms: -8.602325267 + 4 = -4.602325267 b = -4.602325267 Simplifying b = -4.602325267Solution
The solution to the problem is based on the solutions from the subproblems. b = {12.602325267, -4.602325267}
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