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Simplifying (-3b2 + -7b + -4) + (7b2 + 2b + -4) = 0 Reorder the terms: (-4 + -7b + -3b2) + (7b2 + 2b + -4) = 0 Remove parenthesis around (-4 + -7b + -3b2) -4 + -7b + -3b2 + (7b2 + 2b + -4) = 0 Reorder the terms: -4 + -7b + -3b2 + (-4 + 2b + 7b2) = 0 Remove parenthesis around (-4 + 2b + 7b2) -4 + -7b + -3b2 + -4 + 2b + 7b2 = 0 Reorder the terms: -4 + -4 + -7b + 2b + -3b2 + 7b2 = 0 Combine like terms: -4 + -4 = -8 -8 + -7b + 2b + -3b2 + 7b2 = 0 Combine like terms: -7b + 2b = -5b -8 + -5b + -3b2 + 7b2 = 0 Combine like terms: -3b2 + 7b2 = 4b2 -8 + -5b + 4b2 = 0 Solving -8 + -5b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -1.25b + b2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.25b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + -1.25b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.25b + b2 = 0 + 2 -1.25b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.25b + b2 = 2 The b term is -1.25b. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25b + 0.390625 + b2 = 2 + 0.390625 Reorder the terms: 0.390625 + -1.25b + b2 = 2 + 0.390625 Combine like terms: 2 + 0.390625 = 2.390625 0.390625 + -1.25b + b2 = 2.390625 Factor a perfect square on the left side: (b + -0.625)(b + -0.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (b + -0.625) equal to 1.54616461 and -1.54616461.Subproblem 1
b + -0.625 = 1.54616461 Simplifying b + -0.625 = 1.54616461 Reorder the terms: -0.625 + b = 1.54616461 Solving -0.625 + b = 1.54616461 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + b = 1.54616461 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + b = 1.54616461 + 0.625 b = 1.54616461 + 0.625 Combine like terms: 1.54616461 + 0.625 = 2.17116461 b = 2.17116461 Simplifying b = 2.17116461Subproblem 2
b + -0.625 = -1.54616461 Simplifying b + -0.625 = -1.54616461 Reorder the terms: -0.625 + b = -1.54616461 Solving -0.625 + b = -1.54616461 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + b = -1.54616461 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + b = -1.54616461 + 0.625 b = -1.54616461 + 0.625 Combine like terms: -1.54616461 + 0.625 = -0.92116461 b = -0.92116461 Simplifying b = -0.92116461Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.17116461, -0.92116461}
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