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Simplifying b2 + -16b + 64 = 19 Reorder the terms: 64 + -16b + b2 = 19 Solving 64 + -16b + b2 = 19 Solving for variable 'b'. Reorder the terms: 64 + -19 + -16b + b2 = 19 + -19 Combine like terms: 64 + -19 = 45 45 + -16b + b2 = 19 + -19 Combine like terms: 19 + -19 = 0 45 + -16b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -16b + -45 + b2 = 0 + -45 Reorder the terms: 45 + -45 + -16b + b2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -16b + b2 = 0 + -45 -16b + b2 = 0 + -45 Combine like terms: 0 + -45 = -45 -16b + b2 = -45 The b term is -16b. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16b + 64 + b2 = -45 + 64 Reorder the terms: 64 + -16b + b2 = -45 + 64 Combine like terms: -45 + 64 = 19 64 + -16b + b2 = 19 Factor a perfect square on the left side: (b + -8)(b + -8) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (b + -8) equal to 4.358898944 and -4.358898944.Subproblem 1
b + -8 = 4.358898944 Simplifying b + -8 = 4.358898944 Reorder the terms: -8 + b = 4.358898944 Solving -8 + b = 4.358898944 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = 4.358898944 + 8 Combine like terms: -8 + 8 = 0 0 + b = 4.358898944 + 8 b = 4.358898944 + 8 Combine like terms: 4.358898944 + 8 = 12.358898944 b = 12.358898944 Simplifying b = 12.358898944Subproblem 2
b + -8 = -4.358898944 Simplifying b + -8 = -4.358898944 Reorder the terms: -8 + b = -4.358898944 Solving -8 + b = -4.358898944 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = -4.358898944 + 8 Combine like terms: -8 + 8 = 0 0 + b = -4.358898944 + 8 b = -4.358898944 + 8 Combine like terms: -4.358898944 + 8 = 3.641101056 b = 3.641101056 Simplifying b = 3.641101056Solution
The solution to the problem is based on the solutions from the subproblems. b = {12.358898944, 3.641101056}
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