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Simplifying 5b2 + -21b + -16 = 0 Reorder the terms: -16 + -21b + 5b2 = 0 Solving -16 + -21b + 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'. -3.2 + -4.2b + b2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -4.2b + 3.2 + b2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -4.2b + b2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -4.2b + b2 = 0 + 3.2 -4.2b + b2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -4.2b + b2 = 3.2 The b term is -4.2b. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2b + 4.41 + b2 = 3.2 + 4.41 Reorder the terms: 4.41 + -4.2b + b2 = 3.2 + 4.41 Combine like terms: 3.2 + 4.41 = 7.61 4.41 + -4.2b + b2 = 7.61 Factor a perfect square on the left side: (b + -2.1)(b + -2.1) = 7.61 Calculate the square root of the right side: 2.758622845 Break this problem into two subproblems by setting (b + -2.1) equal to 2.758622845 and -2.758622845.Subproblem 1
b + -2.1 = 2.758622845 Simplifying b + -2.1 = 2.758622845 Reorder the terms: -2.1 + b = 2.758622845 Solving -2.1 + b = 2.758622845 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + b = 2.758622845 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + b = 2.758622845 + 2.1 b = 2.758622845 + 2.1 Combine like terms: 2.758622845 + 2.1 = 4.858622845 b = 4.858622845 Simplifying b = 4.858622845Subproblem 2
b + -2.1 = -2.758622845 Simplifying b + -2.1 = -2.758622845 Reorder the terms: -2.1 + b = -2.758622845 Solving -2.1 + b = -2.758622845 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + b = -2.758622845 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + b = -2.758622845 + 2.1 b = -2.758622845 + 2.1 Combine like terms: -2.758622845 + 2.1 = -0.658622845 b = -0.658622845 Simplifying b = -0.658622845Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.858622845, -0.658622845}
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