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Simplifying 7(b + -2) * b = 8 Reorder the terms: 7(-2 + b) * b = 8 Reorder the terms for easier multiplication: 7b(-2 + b) = 8 (-2 * 7b + b * 7b) = 8 (-14b + 7b2) = 8 Solving -14b + 7b2 = 8 Solving for variable 'b'. Reorder the terms: -8 + -14b + 7b2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -14b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -2b + b2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -2b + 1.142857143 + b2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -2b + b2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -2b + b2 = 0 + 1.142857143 -2b + b2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -2b + b2 = 1.142857143 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 1.142857143 + 1 Reorder the terms: 1 + -2b + b2 = 1.142857143 + 1 Combine like terms: 1.142857143 + 1 = 2.142857143 1 + -2b + b2 = 2.142857143 Factor a perfect square on the left side: (b + -1)(b + -1) = 2.142857143 Calculate the square root of the right side: 1.463850109 Break this problem into two subproblems by setting (b + -1) equal to 1.463850109 and -1.463850109.Subproblem 1
b + -1 = 1.463850109 Simplifying b + -1 = 1.463850109 Reorder the terms: -1 + b = 1.463850109 Solving -1 + b = 1.463850109 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 1.463850109 + 1 Combine like terms: -1 + 1 = 0 0 + b = 1.463850109 + 1 b = 1.463850109 + 1 Combine like terms: 1.463850109 + 1 = 2.463850109 b = 2.463850109 Simplifying b = 2.463850109Subproblem 2
b + -1 = -1.463850109 Simplifying b + -1 = -1.463850109 Reorder the terms: -1 + b = -1.463850109 Solving -1 + b = -1.463850109 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -1.463850109 + 1 Combine like terms: -1 + 1 = 0 0 + b = -1.463850109 + 1 b = -1.463850109 + 1 Combine like terms: -1.463850109 + 1 = -0.463850109 b = -0.463850109 Simplifying b = -0.463850109Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.463850109, -0.463850109}
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