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Simplifying 6b2 + -12b + -58 = 0 Reorder the terms: -58 + -12b + 6b2 = 0 Solving -58 + -12b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + -6b + 3b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -6b + 3b2)' equal to zero and attempt to solve: Simplifying -29 + -6b + 3b2 = 0 Solving -29 + -6b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.666666667 + -2b + b2 = 0 Move the constant term to the right: Add '9.666666667' to each side of the equation. -9.666666667 + -2b + 9.666666667 + b2 = 0 + 9.666666667 Reorder the terms: -9.666666667 + 9.666666667 + -2b + b2 = 0 + 9.666666667 Combine like terms: -9.666666667 + 9.666666667 = 0.000000000 0.000000000 + -2b + b2 = 0 + 9.666666667 -2b + b2 = 0 + 9.666666667 Combine like terms: 0 + 9.666666667 = 9.666666667 -2b + b2 = 9.666666667 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 = 9.666666667 + 1 Reorder the terms: 1 + -2b + b2 = 9.666666667 + 1 Combine like terms: 9.666666667 + 1 = 10.666666667 1 + -2b + b2 = 10.666666667 Factor a perfect square on the left side: (b + -1)(b + -1) = 10.666666667 Calculate the square root of the right side: 3.265986324 Break this problem into two subproblems by setting (b + -1) equal to 3.265986324 and -3.265986324.Subproblem 1
b + -1 = 3.265986324 Simplifying b + -1 = 3.265986324 Reorder the terms: -1 + b = 3.265986324 Solving -1 + b = 3.265986324 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 = 3.265986324 + 1 Combine like terms: -1 + 1 = 0 0 + b = 3.265986324 + 1 b = 3.265986324 + 1 Combine like terms: 3.265986324 + 1 = 4.265986324 b = 4.265986324 Simplifying b = 4.265986324Subproblem 2
b + -1 = -3.265986324 Simplifying b + -1 = -3.265986324 Reorder the terms: -1 + b = -3.265986324 Solving -1 + b = -3.265986324 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 = -3.265986324 + 1 Combine like terms: -1 + 1 = 0 0 + b = -3.265986324 + 1 b = -3.265986324 + 1 Combine like terms: -3.265986324 + 1 = -2.265986324 b = -2.265986324 Simplifying b = -2.265986324Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.265986324, -2.265986324}Solution
b = {4.265986324, -2.265986324}
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