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Simplifying 5b2 + -8b + -8 = 0 Reorder the terms: -8 + -8b + 5b2 = 0 Solving -8 + -8b + 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'. -1.6 + -1.6b + b2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -1.6b + 1.6 + b2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -1.6b + b2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -1.6b + b2 = 0 + 1.6 -1.6b + b2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -1.6b + b2 = 1.6 The b term is -1.6b. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6b + 0.64 + b2 = 1.6 + 0.64 Reorder the terms: 0.64 + -1.6b + b2 = 1.6 + 0.64 Combine like terms: 1.6 + 0.64 = 2.24 0.64 + -1.6b + b2 = 2.24 Factor a perfect square on the left side: (b + -0.8)(b + -0.8) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (b + -0.8) equal to 1.496662955 and -1.496662955.Subproblem 1
b + -0.8 = 1.496662955 Simplifying b + -0.8 = 1.496662955 Reorder the terms: -0.8 + b = 1.496662955 Solving -0.8 + b = 1.496662955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + b = 1.496662955 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + b = 1.496662955 + 0.8 b = 1.496662955 + 0.8 Combine like terms: 1.496662955 + 0.8 = 2.296662955 b = 2.296662955 Simplifying b = 2.296662955Subproblem 2
b + -0.8 = -1.496662955 Simplifying b + -0.8 = -1.496662955 Reorder the terms: -0.8 + b = -1.496662955 Solving -0.8 + b = -1.496662955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + b = -1.496662955 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + b = -1.496662955 + 0.8 b = -1.496662955 + 0.8 Combine like terms: -1.496662955 + 0.8 = -0.696662955 b = -0.696662955 Simplifying b = -0.696662955Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.296662955, -0.696662955}
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