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Simplifying b2 + -18b + 18 = 0 Reorder the terms: 18 + -18b + b2 = 0 Solving 18 + -18b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -18b + -18 + b2 = 0 + -18 Reorder the terms: 18 + -18 + -18b + b2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -18b + b2 = 0 + -18 -18b + b2 = 0 + -18 Combine like terms: 0 + -18 = -18 -18b + b2 = -18 The b term is -18b. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18b + 81 + b2 = -18 + 81 Reorder the terms: 81 + -18b + b2 = -18 + 81 Combine like terms: -18 + 81 = 63 81 + -18b + b2 = 63 Factor a perfect square on the left side: (b + -9)(b + -9) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (b + -9) equal to 7.937253933 and -7.937253933.Subproblem 1
b + -9 = 7.937253933 Simplifying b + -9 = 7.937253933 Reorder the terms: -9 + b = 7.937253933 Solving -9 + b = 7.937253933 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + b = 7.937253933 + 9 Combine like terms: -9 + 9 = 0 0 + b = 7.937253933 + 9 b = 7.937253933 + 9 Combine like terms: 7.937253933 + 9 = 16.937253933 b = 16.937253933 Simplifying b = 16.937253933Subproblem 2
b + -9 = -7.937253933 Simplifying b + -9 = -7.937253933 Reorder the terms: -9 + b = -7.937253933 Solving -9 + b = -7.937253933 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + b = -7.937253933 + 9 Combine like terms: -9 + 9 = 0 0 + b = -7.937253933 + 9 b = -7.937253933 + 9 Combine like terms: -7.937253933 + 9 = 1.062746067 b = 1.062746067 Simplifying b = 1.062746067Solution
The solution to the problem is based on the solutions from the subproblems. b = {16.937253933, 1.062746067}
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