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Simplifying 6(b + -4) * b = 5 Reorder the terms: 6(-4 + b) * b = 5 Reorder the terms for easier multiplication: 6b(-4 + b) = 5 (-4 * 6b + b * 6b) = 5 (-24b + 6b2) = 5 Solving -24b + 6b2 = 5 Solving for variable 'b'. Reorder the terms: -5 + -24b + 6b2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -24b + 6b2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -4b + b2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -4b + 0.8333333333 + b2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -4b + b2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -4b + b2 = 0 + 0.8333333333 -4b + b2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -4b + b2 = 0.8333333333 The b term is -4b. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4b + 4 + b2 = 0.8333333333 + 4 Reorder the terms: 4 + -4b + b2 = 0.8333333333 + 4 Combine like terms: 0.8333333333 + 4 = 4.8333333333 4 + -4b + b2 = 4.8333333333 Factor a perfect square on the left side: (b + -2)(b + -2) = 4.8333333333 Calculate the square root of the right side: 2.198484326 Break this problem into two subproblems by setting (b + -2) equal to 2.198484326 and -2.198484326.Subproblem 1
b + -2 = 2.198484326 Simplifying b + -2 = 2.198484326 Reorder the terms: -2 + b = 2.198484326 Solving -2 + b = 2.198484326 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + b = 2.198484326 + 2 Combine like terms: -2 + 2 = 0 0 + b = 2.198484326 + 2 b = 2.198484326 + 2 Combine like terms: 2.198484326 + 2 = 4.198484326 b = 4.198484326 Simplifying b = 4.198484326Subproblem 2
b + -2 = -2.198484326 Simplifying b + -2 = -2.198484326 Reorder the terms: -2 + b = -2.198484326 Solving -2 + b = -2.198484326 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + b = -2.198484326 + 2 Combine like terms: -2 + 2 = 0 0 + b = -2.198484326 + 2 b = -2.198484326 + 2 Combine like terms: -2.198484326 + 2 = -0.198484326 b = -0.198484326 Simplifying b = -0.198484326Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.198484326, -0.198484326}
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