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Simplifying 6b2 = 20 + 10b Solving 6b2 = 20 + 10b Solving for variable 'b'. Reorder the terms: -20 + -10b + 6b2 = 20 + 10b + -20 + -10b Reorder the terms: -20 + -10b + 6b2 = 20 + -20 + 10b + -10b Combine like terms: 20 + -20 = 0 -20 + -10b + 6b2 = 0 + 10b + -10b -20 + -10b + 6b2 = 10b + -10b Combine like terms: 10b + -10b = 0 -20 + -10b + 6b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -5b + 3b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -5b + 3b2)' equal to zero and attempt to solve: Simplifying -10 + -5b + 3b2 = 0 Solving -10 + -5b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -1.666666667b + b2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -1.666666667b + 3.333333333 + b2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -1.666666667b + b2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -1.666666667b + b2 = 0 + 3.333333333 -1.666666667b + b2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -1.666666667b + b2 = 3.333333333 The b term is -1.666666667b. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667b + 0.6944444447 + b2 = 3.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667b + b2 = 3.333333333 + 0.6944444447 Combine like terms: 3.333333333 + 0.6944444447 = 4.0277777777 0.6944444447 + -1.666666667b + b2 = 4.0277777777 Factor a perfect square on the left side: (b + -0.8333333335)(b + -0.8333333335) = 4.0277777777 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (b + -0.8333333335) equal to 2.00693243 and -2.00693243.Subproblem 1
b + -0.8333333335 = 2.00693243 Simplifying b + -0.8333333335 = 2.00693243 Reorder the terms: -0.8333333335 + b = 2.00693243 Solving -0.8333333335 + b = 2.00693243 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + b = 2.00693243 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + b = 2.00693243 + 0.8333333335 b = 2.00693243 + 0.8333333335 Combine like terms: 2.00693243 + 0.8333333335 = 2.8402657635 b = 2.8402657635 Simplifying b = 2.8402657635Subproblem 2
b + -0.8333333335 = -2.00693243 Simplifying b + -0.8333333335 = -2.00693243 Reorder the terms: -0.8333333335 + b = -2.00693243 Solving -0.8333333335 + b = -2.00693243 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + b = -2.00693243 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + b = -2.00693243 + 0.8333333335 b = -2.00693243 + 0.8333333335 Combine like terms: -2.00693243 + 0.8333333335 = -1.1735990965 b = -1.1735990965 Simplifying b = -1.1735990965Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.8402657635, -1.1735990965}Solution
b = {2.8402657635, -1.1735990965}
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