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Simplifying 7b2 + -19b = -6 Reorder the terms: -19b + 7b2 = -6 Solving -19b + 7b2 = -6 Solving for variable 'b'. Reorder the terms: 6 + -19b + 7b2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -19b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + -2.714285714b + b2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -2.714285714b + -0.8571428571 + b2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -2.714285714b + b2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -2.714285714b + b2 = 0 + -0.8571428571 -2.714285714b + b2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -2.714285714b + b2 = -0.8571428571 The b term is -2.714285714b. Take half its coefficient (-1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. -2.714285714b + 1.841836734 + b2 = -0.8571428571 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714b + b2 = -0.8571428571 + 1.841836734 Combine like terms: -0.8571428571 + 1.841836734 = 0.9846938769 1.841836734 + -2.714285714b + b2 = 0.9846938769 Factor a perfect square on the left side: (b + -1.357142857)(b + -1.357142857) = 0.9846938769 Calculate the square root of the right side: 0.992317427 Break this problem into two subproblems by setting (b + -1.357142857) equal to 0.992317427 and -0.992317427.Subproblem 1
b + -1.357142857 = 0.992317427 Simplifying b + -1.357142857 = 0.992317427 Reorder the terms: -1.357142857 + b = 0.992317427 Solving -1.357142857 + b = 0.992317427 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + b = 0.992317427 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + b = 0.992317427 + 1.357142857 b = 0.992317427 + 1.357142857 Combine like terms: 0.992317427 + 1.357142857 = 2.349460284 b = 2.349460284 Simplifying b = 2.349460284Subproblem 2
b + -1.357142857 = -0.992317427 Simplifying b + -1.357142857 = -0.992317427 Reorder the terms: -1.357142857 + b = -0.992317427 Solving -1.357142857 + b = -0.992317427 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + b = -0.992317427 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + b = -0.992317427 + 1.357142857 b = -0.992317427 + 1.357142857 Combine like terms: -0.992317427 + 1.357142857 = 0.36482543 b = 0.36482543 Simplifying b = 0.36482543Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.349460284, 0.36482543}
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