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Simplifying 7b2 = 21 + 9b Solving 7b2 = 21 + 9b Solving for variable 'b'. Reorder the terms: -21 + -9b + 7b2 = 21 + 9b + -21 + -9b Reorder the terms: -21 + -9b + 7b2 = 21 + -21 + 9b + -9b Combine like terms: 21 + -21 = 0 -21 + -9b + 7b2 = 0 + 9b + -9b -21 + -9b + 7b2 = 9b + -9b Combine like terms: 9b + -9b = 0 -21 + -9b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3 + -1.285714286b + b2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.285714286b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + -1.285714286b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.285714286b + b2 = 0 + 3 -1.285714286b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.285714286b + b2 = 3 The b term is -1.285714286b. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286b + 0.4132653063 + b2 = 3 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286b + b2 = 3 + 0.4132653063 Combine like terms: 3 + 0.4132653063 = 3.4132653063 0.4132653063 + -1.285714286b + b2 = 3.4132653063 Factor a perfect square on the left side: (b + -0.642857143)(b + -0.642857143) = 3.4132653063 Calculate the square root of the right side: 1.847502451 Break this problem into two subproblems by setting (b + -0.642857143) equal to 1.847502451 and -1.847502451.Subproblem 1
b + -0.642857143 = 1.847502451 Simplifying b + -0.642857143 = 1.847502451 Reorder the terms: -0.642857143 + b = 1.847502451 Solving -0.642857143 + b = 1.847502451 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + b = 1.847502451 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + b = 1.847502451 + 0.642857143 b = 1.847502451 + 0.642857143 Combine like terms: 1.847502451 + 0.642857143 = 2.490359594 b = 2.490359594 Simplifying b = 2.490359594Subproblem 2
b + -0.642857143 = -1.847502451 Simplifying b + -0.642857143 = -1.847502451 Reorder the terms: -0.642857143 + b = -1.847502451 Solving -0.642857143 + b = -1.847502451 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + b = -1.847502451 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + b = -1.847502451 + 0.642857143 b = -1.847502451 + 0.642857143 Combine like terms: -1.847502451 + 0.642857143 = -1.204645308 b = -1.204645308 Simplifying b = -1.204645308Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.490359594, -1.204645308}
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