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Simplifying 5b2 + 22b + 22 = 0 Reorder the terms: 22 + 22b + 5b2 = 0 Solving 22 + 22b + 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'. 4.4 + 4.4b + b2 = 0 Move the constant term to the right: Add '-4.4' to each side of the equation. 4.4 + 4.4b + -4.4 + b2 = 0 + -4.4 Reorder the terms: 4.4 + -4.4 + 4.4b + b2 = 0 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + 4.4b + b2 = 0 + -4.4 4.4b + b2 = 0 + -4.4 Combine like terms: 0 + -4.4 = -4.4 4.4b + b2 = -4.4 The b term is 4.4b. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4b + 4.84 + b2 = -4.4 + 4.84 Reorder the terms: 4.84 + 4.4b + b2 = -4.4 + 4.84 Combine like terms: -4.4 + 4.84 = 0.44 4.84 + 4.4b + b2 = 0.44 Factor a perfect square on the left side: (b + 2.2)(b + 2.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (b + 2.2) equal to 0.663324958 and -0.663324958.Subproblem 1
b + 2.2 = 0.663324958 Simplifying b + 2.2 = 0.663324958 Reorder the terms: 2.2 + b = 0.663324958 Solving 2.2 + b = 0.663324958 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + b = 0.663324958 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + b = 0.663324958 + -2.2 b = 0.663324958 + -2.2 Combine like terms: 0.663324958 + -2.2 = -1.536675042 b = -1.536675042 Simplifying b = -1.536675042Subproblem 2
b + 2.2 = -0.663324958 Simplifying b + 2.2 = -0.663324958 Reorder the terms: 2.2 + b = -0.663324958 Solving 2.2 + b = -0.663324958 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + b = -0.663324958 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + b = -0.663324958 + -2.2 b = -0.663324958 + -2.2 Combine like terms: -0.663324958 + -2.2 = -2.863324958 b = -2.863324958 Simplifying b = -2.863324958Solution
The solution to the problem is based on the solutions from the subproblems. b = {-1.536675042, -2.863324958}
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