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Simplifying 932.23 = b2 + -32b Reorder the terms: 932.23 = -32b + b2 Solving 932.23 = -32b + b2 Solving for variable 'b'. Reorder the terms: 932.23 + 32b + -1b2 = -32b + 32b + b2 + -1b2 Combine like terms: -32b + 32b = 0 932.23 + 32b + -1b2 = 0 + b2 + -1b2 932.23 + 32b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 932.23 + 32b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -932.23 + -32b + b2 = 0 Move the constant term to the right: Add '932.23' to each side of the equation. -932.23 + -32b + 932.23 + b2 = 0 + 932.23 Reorder the terms: -932.23 + 932.23 + -32b + b2 = 0 + 932.23 Combine like terms: -932.23 + 932.23 = 0.00 0.00 + -32b + b2 = 0 + 932.23 -32b + b2 = 0 + 932.23 Combine like terms: 0 + 932.23 = 932.23 -32b + b2 = 932.23 The b term is -32b. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32b + 256 + b2 = 932.23 + 256 Reorder the terms: 256 + -32b + b2 = 932.23 + 256 Combine like terms: 932.23 + 256 = 1188.23 256 + -32b + b2 = 1188.23 Factor a perfect square on the left side: (b + -16)(b + -16) = 1188.23 Calculate the square root of the right side: 34.470712206 Break this problem into two subproblems by setting (b + -16) equal to 34.470712206 and -34.470712206.Subproblem 1
b + -16 = 34.470712206 Simplifying b + -16 = 34.470712206 Reorder the terms: -16 + b = 34.470712206 Solving -16 + b = 34.470712206 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + b = 34.470712206 + 16 Combine like terms: -16 + 16 = 0 0 + b = 34.470712206 + 16 b = 34.470712206 + 16 Combine like terms: 34.470712206 + 16 = 50.470712206 b = 50.470712206 Simplifying b = 50.470712206Subproblem 2
b + -16 = -34.470712206 Simplifying b + -16 = -34.470712206 Reorder the terms: -16 + b = -34.470712206 Solving -16 + b = -34.470712206 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + b = -34.470712206 + 16 Combine like terms: -16 + 16 = 0 0 + b = -34.470712206 + 16 b = -34.470712206 + 16 Combine like terms: -34.470712206 + 16 = -18.470712206 b = -18.470712206 Simplifying b = -18.470712206Solution
The solution to the problem is based on the solutions from the subproblems. b = {50.470712206, -18.470712206}
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