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Simplifying 5b2 + 10b + -49 = 0 Reorder the terms: -49 + 10b + 5b2 = 0 Solving -49 + 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'. -9.8 + 2b + b2 = 0 Move the constant term to the right: Add '9.8' to each side of the equation. -9.8 + 2b + 9.8 + b2 = 0 + 9.8 Reorder the terms: -9.8 + 9.8 + 2b + b2 = 0 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + 2b + b2 = 0 + 9.8 2b + b2 = 0 + 9.8 Combine like terms: 0 + 9.8 = 9.8 2b + b2 = 9.8 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 = 9.8 + 1 Reorder the terms: 1 + 2b + b2 = 9.8 + 1 Combine like terms: 9.8 + 1 = 10.8 1 + 2b + b2 = 10.8 Factor a perfect square on the left side: (b + 1)(b + 1) = 10.8 Calculate the square root of the right side: 3.286335345 Break this problem into two subproblems by setting (b + 1) equal to 3.286335345 and -3.286335345.Subproblem 1
b + 1 = 3.286335345 Simplifying b + 1 = 3.286335345 Reorder the terms: 1 + b = 3.286335345 Solving 1 + b = 3.286335345 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 = 3.286335345 + -1 Combine like terms: 1 + -1 = 0 0 + b = 3.286335345 + -1 b = 3.286335345 + -1 Combine like terms: 3.286335345 + -1 = 2.286335345 b = 2.286335345 Simplifying b = 2.286335345Subproblem 2
b + 1 = -3.286335345 Simplifying b + 1 = -3.286335345 Reorder the terms: 1 + b = -3.286335345 Solving 1 + b = -3.286335345 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 = -3.286335345 + -1 Combine like terms: 1 + -1 = 0 0 + b = -3.286335345 + -1 b = -3.286335345 + -1 Combine like terms: -3.286335345 + -1 = -4.286335345 b = -4.286335345 Simplifying b = -4.286335345Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.286335345, -4.286335345}
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