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Simplifying 4b2 + -8b = 72 Reorder the terms: -8b + 4b2 = 72 Solving -8b + 4b2 = 72 Solving for variable 'b'. Reorder the terms: -72 + -8b + 4b2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + -8b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-18 + -2b + b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-18 + -2b + b2)' equal to zero and attempt to solve: Simplifying -18 + -2b + b2 = 0 Solving -18 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -2b + 18 + b2 = 0 + 18 Reorder the terms: -18 + 18 + -2b + b2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2b + b2 = 0 + 18 -2b + b2 = 0 + 18 Combine like terms: 0 + 18 = 18 -2b + b2 = 18 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 = 18 + 1 Reorder the terms: 1 + -2b + b2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + -2b + b2 = 19 Factor a perfect square on the left side: (b + -1)(b + -1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (b + -1) equal to 4.358898944 and -4.358898944.Subproblem 1
b + -1 = 4.358898944 Simplifying b + -1 = 4.358898944 Reorder the terms: -1 + b = 4.358898944 Solving -1 + b = 4.358898944 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 = 4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + b = 4.358898944 + 1 b = 4.358898944 + 1 Combine like terms: 4.358898944 + 1 = 5.358898944 b = 5.358898944 Simplifying b = 5.358898944Subproblem 2
b + -1 = -4.358898944 Simplifying b + -1 = -4.358898944 Reorder the terms: -1 + b = -4.358898944 Solving -1 + b = -4.358898944 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 = -4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + b = -4.358898944 + 1 b = -4.358898944 + 1 Combine like terms: -4.358898944 + 1 = -3.358898944 b = -3.358898944 Simplifying b = -3.358898944Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.358898944, -3.358898944}Solution
b = {5.358898944, -3.358898944}
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