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Simplifying b2 + -9b + -7 = 0 Reorder the terms: -7 + -9b + b2 = 0 Solving -7 + -9b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -9b + 7 + b2 = 0 + 7 Reorder the terms: -7 + 7 + -9b + b2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9b + b2 = 0 + 7 -9b + b2 = 0 + 7 Combine like terms: 0 + 7 = 7 -9b + b2 = 7 The b term is -9b. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9b + 20.25 + b2 = 7 + 20.25 Reorder the terms: 20.25 + -9b + b2 = 7 + 20.25 Combine like terms: 7 + 20.25 = 27.25 20.25 + -9b + b2 = 27.25 Factor a perfect square on the left side: (b + -4.5)(b + -4.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (b + -4.5) equal to 5.220153254 and -5.220153254.Subproblem 1
b + -4.5 = 5.220153254 Simplifying b + -4.5 = 5.220153254 Reorder the terms: -4.5 + b = 5.220153254 Solving -4.5 + b = 5.220153254 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + b = 5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + b = 5.220153254 + 4.5 b = 5.220153254 + 4.5 Combine like terms: 5.220153254 + 4.5 = 9.720153254 b = 9.720153254 Simplifying b = 9.720153254Subproblem 2
b + -4.5 = -5.220153254 Simplifying b + -4.5 = -5.220153254 Reorder the terms: -4.5 + b = -5.220153254 Solving -4.5 + b = -5.220153254 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + b = -5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + b = -5.220153254 + 4.5 b = -5.220153254 + 4.5 Combine like terms: -5.220153254 + 4.5 = -0.720153254 b = -0.720153254 Simplifying b = -0.720153254Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.720153254, -0.720153254}
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