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Simplifying 8b2 + 11b + -11 = 6 Reorder the terms: -11 + 11b + 8b2 = 6 Solving -11 + 11b + 8b2 = 6 Solving for variable 'b'. Reorder the terms: -11 + -6 + 11b + 8b2 = 6 + -6 Combine like terms: -11 + -6 = -17 -17 + 11b + 8b2 = 6 + -6 Combine like terms: 6 + -6 = 0 -17 + 11b + 8b2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.125 + 1.375b + b2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + 1.375b + 2.125 + b2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + 1.375b + b2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + 1.375b + b2 = 0 + 2.125 1.375b + b2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 1.375b + b2 = 2.125 The b term is 1.375b. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375b + 0.47265625 + b2 = 2.125 + 0.47265625 Reorder the terms: 0.47265625 + 1.375b + b2 = 2.125 + 0.47265625 Combine like terms: 2.125 + 0.47265625 = 2.59765625 0.47265625 + 1.375b + b2 = 2.59765625 Factor a perfect square on the left side: (b + 0.6875)(b + 0.6875) = 2.59765625 Calculate the square root of the right side: 1.61172462 Break this problem into two subproblems by setting (b + 0.6875) equal to 1.61172462 and -1.61172462.Subproblem 1
b + 0.6875 = 1.61172462 Simplifying b + 0.6875 = 1.61172462 Reorder the terms: 0.6875 + b = 1.61172462 Solving 0.6875 + b = 1.61172462 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + b = 1.61172462 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + b = 1.61172462 + -0.6875 b = 1.61172462 + -0.6875 Combine like terms: 1.61172462 + -0.6875 = 0.92422462 b = 0.92422462 Simplifying b = 0.92422462Subproblem 2
b + 0.6875 = -1.61172462 Simplifying b + 0.6875 = -1.61172462 Reorder the terms: 0.6875 + b = -1.61172462 Solving 0.6875 + b = -1.61172462 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + b = -1.61172462 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + b = -1.61172462 + -0.6875 b = -1.61172462 + -0.6875 Combine like terms: -1.61172462 + -0.6875 = -2.29922462 b = -2.29922462 Simplifying b = -2.29922462Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.92422462, -2.29922462}
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