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Simplifying b2 + 20b = -90 Reorder the terms: 20b + b2 = -90 Solving 20b + b2 = -90 Solving for variable 'b'. Reorder the terms: 90 + 20b + b2 = -90 + 90 Combine like terms: -90 + 90 = 0 90 + 20b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + 20b + -90 + b2 = 0 + -90 Reorder the terms: 90 + -90 + 20b + b2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 20b + b2 = 0 + -90 20b + b2 = 0 + -90 Combine like terms: 0 + -90 = -90 20b + b2 = -90 The b term is 20b. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20b + 100 + b2 = -90 + 100 Reorder the terms: 100 + 20b + b2 = -90 + 100 Combine like terms: -90 + 100 = 10 100 + 20b + b2 = 10 Factor a perfect square on the left side: (b + 10)(b + 10) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (b + 10) equal to 3.16227766 and -3.16227766.Subproblem 1
b + 10 = 3.16227766 Simplifying b + 10 = 3.16227766 Reorder the terms: 10 + b = 3.16227766 Solving 10 + b = 3.16227766 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + b = 3.16227766 + -10 Combine like terms: 10 + -10 = 0 0 + b = 3.16227766 + -10 b = 3.16227766 + -10 Combine like terms: 3.16227766 + -10 = -6.83772234 b = -6.83772234 Simplifying b = -6.83772234Subproblem 2
b + 10 = -3.16227766 Simplifying b + 10 = -3.16227766 Reorder the terms: 10 + b = -3.16227766 Solving 10 + b = -3.16227766 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + b = -3.16227766 + -10 Combine like terms: 10 + -10 = 0 0 + b = -3.16227766 + -10 b = -3.16227766 + -10 Combine like terms: -3.16227766 + -10 = -13.16227766 b = -13.16227766 Simplifying b = -13.16227766Solution
The solution to the problem is based on the solutions from the subproblems. b = {-6.83772234, -13.16227766}
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