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Simplifying 7b2 + -6b + -4 = 0 Reorder the terms: -4 + -6b + 7b2 = 0 Solving -4 + -6b + 7b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + -0.8571428571b + b2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.8571428571b + 0.5714285714 + b2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.8571428571b + b2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.8571428571b + b2 = 0 + 0.5714285714 -0.8571428571b + b2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.8571428571b + b2 = 0.5714285714 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 = 0.5714285714 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571b + b2 = 0.5714285714 + 0.1836734694 Combine like terms: 0.5714285714 + 0.1836734694 = 0.7551020408 0.1836734694 + -0.8571428571b + b2 = 0.7551020408 Factor a perfect square on the left side: (b + -0.4285714286)(b + -0.4285714286) = 0.7551020408 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (b + -0.4285714286) equal to 0.868966076 and -0.868966076.Subproblem 1
b + -0.4285714286 = 0.868966076 Simplifying b + -0.4285714286 = 0.868966076 Reorder the terms: -0.4285714286 + b = 0.868966076 Solving -0.4285714286 + b = 0.868966076 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 = 0.868966076 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + b = 0.868966076 + 0.4285714286 b = 0.868966076 + 0.4285714286 Combine like terms: 0.868966076 + 0.4285714286 = 1.2975375046 b = 1.2975375046 Simplifying b = 1.2975375046Subproblem 2
b + -0.4285714286 = -0.868966076 Simplifying b + -0.4285714286 = -0.868966076 Reorder the terms: -0.4285714286 + b = -0.868966076 Solving -0.4285714286 + b = -0.868966076 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 = -0.868966076 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + b = -0.868966076 + 0.4285714286 b = -0.868966076 + 0.4285714286 Combine like terms: -0.868966076 + 0.4285714286 = -0.4403946474 b = -0.4403946474 Simplifying b = -0.4403946474Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.2975375046, -0.4403946474}
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