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Simplifying 5b2 + -10b + -168 = 0 Reorder the terms: -168 + -10b + 5b2 = 0 Solving -168 + -10b + 5b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -33.6 + -2b + b2 = 0 Move the constant term to the right: Add '33.6' to each side of the equation. -33.6 + -2b + 33.6 + b2 = 0 + 33.6 Reorder the terms: -33.6 + 33.6 + -2b + b2 = 0 + 33.6 Combine like terms: -33.6 + 33.6 = 0.0 0.0 + -2b + b2 = 0 + 33.6 -2b + b2 = 0 + 33.6 Combine like terms: 0 + 33.6 = 33.6 -2b + b2 = 33.6 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 = 33.6 + 1 Reorder the terms: 1 + -2b + b2 = 33.6 + 1 Combine like terms: 33.6 + 1 = 34.6 1 + -2b + b2 = 34.6 Factor a perfect square on the left side: (b + -1)(b + -1) = 34.6 Calculate the square root of the right side: 5.882176468 Break this problem into two subproblems by setting (b + -1) equal to 5.882176468 and -5.882176468.Subproblem 1
b + -1 = 5.882176468 Simplifying b + -1 = 5.882176468 Reorder the terms: -1 + b = 5.882176468 Solving -1 + b = 5.882176468 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 = 5.882176468 + 1 Combine like terms: -1 + 1 = 0 0 + b = 5.882176468 + 1 b = 5.882176468 + 1 Combine like terms: 5.882176468 + 1 = 6.882176468 b = 6.882176468 Simplifying b = 6.882176468Subproblem 2
b + -1 = -5.882176468 Simplifying b + -1 = -5.882176468 Reorder the terms: -1 + b = -5.882176468 Solving -1 + b = -5.882176468 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 = -5.882176468 + 1 Combine like terms: -1 + 1 = 0 0 + b = -5.882176468 + 1 b = -5.882176468 + 1 Combine like terms: -5.882176468 + 1 = -4.882176468 b = -4.882176468 Simplifying b = -4.882176468Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.882176468, -4.882176468}
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