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Simplifying 7b2 + -6b + -4 = 3 Reorder the terms: -4 + -6b + 7b2 = 3 Solving -4 + -6b + 7b2 = 3 Solving for variable 'b'. Reorder the terms: -4 + -3 + -6b + 7b2 = 3 + -3 Combine like terms: -4 + -3 = -7 -7 + -6b + 7b2 = 3 + -3 Combine like terms: 3 + -3 = 0 -7 + -6b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + -0.8571428571b + b2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.8571428571b + 1 + b2 = 0 + 1 Reorder the terms: -1 + 1 + -0.8571428571b + b2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.8571428571b + b2 = 0 + 1 -0.8571428571b + b2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.8571428571b + b2 = 1 The b term is -0.8571428571b. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571b + 0.1836734694 + b2 = 1 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571b + b2 = 1 + 0.1836734694 Combine like terms: 1 + 0.1836734694 = 1.1836734694 0.1836734694 + -0.8571428571b + b2 = 1.1836734694 Factor a perfect square on the left side: (b + -0.4285714286)(b + -0.4285714286) = 1.1836734694 Calculate the square root of the right side: 1.087967587 Break this problem into two subproblems by setting (b + -0.4285714286) equal to 1.087967587 and -1.087967587.Subproblem 1
b + -0.4285714286 = 1.087967587 Simplifying b + -0.4285714286 = 1.087967587 Reorder the terms: -0.4285714286 + b = 1.087967587 Solving -0.4285714286 + b = 1.087967587 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + b = 1.087967587 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + b = 1.087967587 + 0.4285714286 b = 1.087967587 + 0.4285714286 Combine like terms: 1.087967587 + 0.4285714286 = 1.5165390156 b = 1.5165390156 Simplifying b = 1.5165390156Subproblem 2
b + -0.4285714286 = -1.087967587 Simplifying b + -0.4285714286 = -1.087967587 Reorder the terms: -0.4285714286 + b = -1.087967587 Solving -0.4285714286 + b = -1.087967587 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + b = -1.087967587 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + b = -1.087967587 + 0.4285714286 b = -1.087967587 + 0.4285714286 Combine like terms: -1.087967587 + 0.4285714286 = -0.6593961584 b = -0.6593961584 Simplifying b = -0.6593961584Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.5165390156, -0.6593961584}
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