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Simplifying 3b(b + -4) + 6(b + -8) = 0 Reorder the terms: 3b(-4 + b) + 6(b + -8) = 0 (-4 * 3b + b * 3b) + 6(b + -8) = 0 (-12b + 3b2) + 6(b + -8) = 0 Reorder the terms: -12b + 3b2 + 6(-8 + b) = 0 -12b + 3b2 + (-8 * 6 + b * 6) = 0 -12b + 3b2 + (-48 + 6b) = 0 Reorder the terms: -48 + -12b + 6b + 3b2 = 0 Combine like terms: -12b + 6b = -6b -48 + -6b + 3b2 = 0 Solving -48 + -6b + 3b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + -2b + b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-16 + -2b + b2)' equal to zero and attempt to solve: Simplifying -16 + -2b + b2 = 0 Solving -16 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -2b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + -2b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2b + b2 = 0 + 16 -2b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 -2b + b2 = 16 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 = 16 + 1 Reorder the terms: 1 + -2b + b2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + -2b + b2 = 17 Factor a perfect square on the left side: (b + -1)(b + -1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (b + -1) equal to 4.123105626 and -4.123105626.Subproblem 1
b + -1 = 4.123105626 Simplifying b + -1 = 4.123105626 Reorder the terms: -1 + b = 4.123105626 Solving -1 + b = 4.123105626 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 = 4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + b = 4.123105626 + 1 b = 4.123105626 + 1 Combine like terms: 4.123105626 + 1 = 5.123105626 b = 5.123105626 Simplifying b = 5.123105626Subproblem 2
b + -1 = -4.123105626 Simplifying b + -1 = -4.123105626 Reorder the terms: -1 + b = -4.123105626 Solving -1 + b = -4.123105626 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 = -4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + b = -4.123105626 + 1 b = -4.123105626 + 1 Combine like terms: -4.123105626 + 1 = -3.123105626 b = -3.123105626 Simplifying b = -3.123105626Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.123105626, -3.123105626}Solution
b = {5.123105626, -3.123105626}
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