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Simplifying 44b2 + -126b + -48 = 0 Reorder the terms: -48 + -126b + 44b2 = 0 Solving -48 + -126b + 44b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -63b + 22b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + -63b + 22b2)' equal to zero and attempt to solve: Simplifying -24 + -63b + 22b2 = 0 Solving -24 + -63b + 22b2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -1.090909091 + -2.863636364b + b2 = 0 Move the constant term to the right: Add '1.090909091' to each side of the equation. -1.090909091 + -2.863636364b + 1.090909091 + b2 = 0 + 1.090909091 Reorder the terms: -1.090909091 + 1.090909091 + -2.863636364b + b2 = 0 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + -2.863636364b + b2 = 0 + 1.090909091 -2.863636364b + b2 = 0 + 1.090909091 Combine like terms: 0 + 1.090909091 = 1.090909091 -2.863636364b + b2 = 1.090909091 The b term is -2.863636364b. Take half its coefficient (-1.431818182). Square it (2.050103306) and add it to both sides. Add '2.050103306' to each side of the equation. -2.863636364b + 2.050103306 + b2 = 1.090909091 + 2.050103306 Reorder the terms: 2.050103306 + -2.863636364b + b2 = 1.090909091 + 2.050103306 Combine like terms: 1.090909091 + 2.050103306 = 3.141012397 2.050103306 + -2.863636364b + b2 = 3.141012397 Factor a perfect square on the left side: (b + -1.431818182)(b + -1.431818182) = 3.141012397 Calculate the square root of the right side: 1.772290156 Break this problem into two subproblems by setting (b + -1.431818182) equal to 1.772290156 and -1.772290156.Subproblem 1
b + -1.431818182 = 1.772290156 Simplifying b + -1.431818182 = 1.772290156 Reorder the terms: -1.431818182 + b = 1.772290156 Solving -1.431818182 + b = 1.772290156 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.431818182' to each side of the equation. -1.431818182 + 1.431818182 + b = 1.772290156 + 1.431818182 Combine like terms: -1.431818182 + 1.431818182 = 0.000000000 0.000000000 + b = 1.772290156 + 1.431818182 b = 1.772290156 + 1.431818182 Combine like terms: 1.772290156 + 1.431818182 = 3.204108338 b = 3.204108338 Simplifying b = 3.204108338Subproblem 2
b + -1.431818182 = -1.772290156 Simplifying b + -1.431818182 = -1.772290156 Reorder the terms: -1.431818182 + b = -1.772290156 Solving -1.431818182 + b = -1.772290156 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.431818182' to each side of the equation. -1.431818182 + 1.431818182 + b = -1.772290156 + 1.431818182 Combine like terms: -1.431818182 + 1.431818182 = 0.000000000 0.000000000 + b = -1.772290156 + 1.431818182 b = -1.772290156 + 1.431818182 Combine like terms: -1.772290156 + 1.431818182 = -0.340471974 b = -0.340471974 Simplifying b = -0.340471974Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.204108338, -0.340471974}Solution
b = {3.204108338, -0.340471974}
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