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Simplifying b2 + 30b + -10 = 0 Reorder the terms: -10 + 30b + b2 = 0 Solving -10 + 30b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 30b + 10 + b2 = 0 + 10 Reorder the terms: -10 + 10 + 30b + b2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 30b + b2 = 0 + 10 30b + b2 = 0 + 10 Combine like terms: 0 + 10 = 10 30b + b2 = 10 The b term is 30b. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30b + 225 + b2 = 10 + 225 Reorder the terms: 225 + 30b + b2 = 10 + 225 Combine like terms: 10 + 225 = 235 225 + 30b + b2 = 235 Factor a perfect square on the left side: (b + 15)(b + 15) = 235 Calculate the square root of the right side: 15.329709717 Break this problem into two subproblems by setting (b + 15) equal to 15.329709717 and -15.329709717.Subproblem 1
b + 15 = 15.329709717 Simplifying b + 15 = 15.329709717 Reorder the terms: 15 + b = 15.329709717 Solving 15 + b = 15.329709717 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + b = 15.329709717 + -15 Combine like terms: 15 + -15 = 0 0 + b = 15.329709717 + -15 b = 15.329709717 + -15 Combine like terms: 15.329709717 + -15 = 0.329709717 b = 0.329709717 Simplifying b = 0.329709717Subproblem 2
b + 15 = -15.329709717 Simplifying b + 15 = -15.329709717 Reorder the terms: 15 + b = -15.329709717 Solving 15 + b = -15.329709717 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + b = -15.329709717 + -15 Combine like terms: 15 + -15 = 0 0 + b = -15.329709717 + -15 b = -15.329709717 + -15 Combine like terms: -15.329709717 + -15 = -30.329709717 b = -30.329709717 Simplifying b = -30.329709717Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.329709717, -30.329709717}
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