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Simplifying 5b2 + -4b + -15 = 0 Reorder the terms: -15 + -4b + 5b2 = 0 Solving -15 + -4b + 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 + -0.8b + b2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.8b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + -0.8b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.8b + b2 = 0 + 3 -0.8b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.8b + b2 = 3 The b term is -0.8b. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8b + 0.16 + b2 = 3 + 0.16 Reorder the terms: 0.16 + -0.8b + b2 = 3 + 0.16 Combine like terms: 3 + 0.16 = 3.16 0.16 + -0.8b + b2 = 3.16 Factor a perfect square on the left side: (b + -0.4)(b + -0.4) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (b + -0.4) equal to 1.777638883 and -1.777638883.Subproblem 1
b + -0.4 = 1.777638883 Simplifying b + -0.4 = 1.777638883 Reorder the terms: -0.4 + b = 1.777638883 Solving -0.4 + b = 1.777638883 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + b = 1.777638883 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + b = 1.777638883 + 0.4 b = 1.777638883 + 0.4 Combine like terms: 1.777638883 + 0.4 = 2.177638883 b = 2.177638883 Simplifying b = 2.177638883Subproblem 2
b + -0.4 = -1.777638883 Simplifying b + -0.4 = -1.777638883 Reorder the terms: -0.4 + b = -1.777638883 Solving -0.4 + b = -1.777638883 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + b = -1.777638883 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + b = -1.777638883 + 0.4 b = -1.777638883 + 0.4 Combine like terms: -1.777638883 + 0.4 = -1.377638883 b = -1.377638883 Simplifying b = -1.377638883Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.177638883, -1.377638883}
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