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Simplifying 10b2 + -20b + -27 = -7 Reorder the terms: -27 + -20b + 10b2 = -7 Solving -27 + -20b + 10b2 = -7 Solving for variable 'b'. Reorder the terms: -27 + 7 + -20b + 10b2 = -7 + 7 Combine like terms: -27 + 7 = -20 -20 + -20b + 10b2 = -7 + 7 Combine like terms: -7 + 7 = 0 -20 + -20b + 10b2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-2 + -2b + b2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-2 + -2b + b2)' equal to zero and attempt to solve: Simplifying -2 + -2b + b2 = 0 Solving -2 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + -2b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2b + b2 = 0 + 2 -2b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2b + b2 = 2 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 2 + 1 Reorder the terms: 1 + -2b + b2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2b + b2 = 3 Factor a perfect square on the left side: (b + -1)(b + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (b + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
b + -1 = 1.732050808 Simplifying b + -1 = 1.732050808 Reorder the terms: -1 + b = 1.732050808 Solving -1 + b = 1.732050808 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + b = 1.732050808 + 1 b = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 b = 2.732050808 Simplifying b = 2.732050808Subproblem 2
b + -1 = -1.732050808 Simplifying b + -1 = -1.732050808 Reorder the terms: -1 + b = -1.732050808 Solving -1 + b = -1.732050808 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + b = -1.732050808 + 1 b = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 b = -0.732050808 Simplifying b = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.732050808, -0.732050808}Solution
b = {2.732050808, -0.732050808}
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