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Simplifying 44b2 + -228b + -140 = 0 Reorder the terms: -140 + -228b + 44b2 = 0 Solving -140 + -228b + 44b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(-35 + -57b + 11b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-35 + -57b + 11b2)' equal to zero and attempt to solve: Simplifying -35 + -57b + 11b2 = 0 Solving -35 + -57b + 11b2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -3.181818182 + -5.181818182b + b2 = 0 Move the constant term to the right: Add '3.181818182' to each side of the equation. -3.181818182 + -5.181818182b + 3.181818182 + b2 = 0 + 3.181818182 Reorder the terms: -3.181818182 + 3.181818182 + -5.181818182b + b2 = 0 + 3.181818182 Combine like terms: -3.181818182 + 3.181818182 = 0.000000000 0.000000000 + -5.181818182b + b2 = 0 + 3.181818182 -5.181818182b + b2 = 0 + 3.181818182 Combine like terms: 0 + 3.181818182 = 3.181818182 -5.181818182b + b2 = 3.181818182 The b term is -5.181818182b. Take half its coefficient (-2.590909091). Square it (6.712809918) and add it to both sides. Add '6.712809918' to each side of the equation. -5.181818182b + 6.712809918 + b2 = 3.181818182 + 6.712809918 Reorder the terms: 6.712809918 + -5.181818182b + b2 = 3.181818182 + 6.712809918 Combine like terms: 3.181818182 + 6.712809918 = 9.8946281 6.712809918 + -5.181818182b + b2 = 9.8946281 Factor a perfect square on the left side: (b + -2.590909091)(b + -2.590909091) = 9.8946281 Calculate the square root of the right side: 3.145572778 Break this problem into two subproblems by setting (b + -2.590909091) equal to 3.145572778 and -3.145572778.Subproblem 1
b + -2.590909091 = 3.145572778 Simplifying b + -2.590909091 = 3.145572778 Reorder the terms: -2.590909091 + b = 3.145572778 Solving -2.590909091 + b = 3.145572778 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.590909091' to each side of the equation. -2.590909091 + 2.590909091 + b = 3.145572778 + 2.590909091 Combine like terms: -2.590909091 + 2.590909091 = 0.000000000 0.000000000 + b = 3.145572778 + 2.590909091 b = 3.145572778 + 2.590909091 Combine like terms: 3.145572778 + 2.590909091 = 5.736481869 b = 5.736481869 Simplifying b = 5.736481869Subproblem 2
b + -2.590909091 = -3.145572778 Simplifying b + -2.590909091 = -3.145572778 Reorder the terms: -2.590909091 + b = -3.145572778 Solving -2.590909091 + b = -3.145572778 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.590909091' to each side of the equation. -2.590909091 + 2.590909091 + b = -3.145572778 + 2.590909091 Combine like terms: -2.590909091 + 2.590909091 = 0.000000000 0.000000000 + b = -3.145572778 + 2.590909091 b = -3.145572778 + 2.590909091 Combine like terms: -3.145572778 + 2.590909091 = -0.554663687 b = -0.554663687 Simplifying b = -0.554663687Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.736481869, -0.554663687}Solution
b = {5.736481869, -0.554663687}
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