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Simplifying 10b2 + 33b + -12 = 0 Reorder the terms: -12 + 33b + 10b2 = 0 Solving -12 + 33b + 10b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + 3.3b + b2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 3.3b + 1.2 + b2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 3.3b + b2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 3.3b + b2 = 0 + 1.2 3.3b + b2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 3.3b + b2 = 1.2 The b term is 3.3b. Take half its coefficient (1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. 3.3b + 2.7225 + b2 = 1.2 + 2.7225 Reorder the terms: 2.7225 + 3.3b + b2 = 1.2 + 2.7225 Combine like terms: 1.2 + 2.7225 = 3.9225 2.7225 + 3.3b + b2 = 3.9225 Factor a perfect square on the left side: (b + 1.65)(b + 1.65) = 3.9225 Calculate the square root of the right side: 1.980530232 Break this problem into two subproblems by setting (b + 1.65) equal to 1.980530232 and -1.980530232.Subproblem 1
b + 1.65 = 1.980530232 Simplifying b + 1.65 = 1.980530232 Reorder the terms: 1.65 + b = 1.980530232 Solving 1.65 + b = 1.980530232 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + b = 1.980530232 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + b = 1.980530232 + -1.65 b = 1.980530232 + -1.65 Combine like terms: 1.980530232 + -1.65 = 0.330530232 b = 0.330530232 Simplifying b = 0.330530232Subproblem 2
b + 1.65 = -1.980530232 Simplifying b + 1.65 = -1.980530232 Reorder the terms: 1.65 + b = -1.980530232 Solving 1.65 + b = -1.980530232 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + b = -1.980530232 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + b = -1.980530232 + -1.65 b = -1.980530232 + -1.65 Combine like terms: -1.980530232 + -1.65 = -3.630530232 b = -3.630530232 Simplifying b = -3.630530232Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.330530232, -3.630530232}
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