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Simplifying (20b * 20b) + -17b = 63 Reorder the terms for easier multiplication: (20 * 20b * b) + -17b = 63 Multiply 20 * 20 (400b * b) + -17b = 63 Multiply b * b (400b2) + -17b = 63 Reorder the terms: -17b + (400b2) = 63 Solving -17b + (400b2) = 63 Solving for variable 'b'. Reorder the terms: -63 + -17b + (400b2) = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -17b + (400b2) = 0 Begin completing the square. Divide all terms by 400 the coefficient of the squared term: Divide each side by '400'. -0.1575 + -0.0425b + b2 = 0.00 Move the constant term to the right: Add '0.1575' to each side of the equation. -0.1575 + -0.0425b + 0.1575 + b2 = 0.00 + 0.1575 Reorder the terms: -0.1575 + 0.1575 + -0.0425b + b2 = 0.00 + 0.1575 Combine like terms: -0.1575 + 0.1575 = 0.0000 0.0000 + -0.0425b + b2 = 0.00 + 0.1575 -0.0425b + b2 = 0.00 + 0.1575 Combine like terms: 0.00 + 0.1575 = 0.1575 -0.0425b + b2 = 0.1575 The b term is -0.0425b. Take half its coefficient (-0.02125). Square it (0.0004515625) and add it to both sides. Add '0.0004515625' to each side of the equation. -0.0425b + 0.0004515625 + b2 = 0.1575 + 0.0004515625 Reorder the terms: 0.0004515625 + -0.0425b + b2 = 0.1575 + 0.0004515625 Combine like terms: 0.1575 + 0.0004515625 = 0.1579515625 0.0004515625 + -0.0425b + b2 = 0.1579515625 Factor a perfect square on the left side: ((b) + -0.02125)((b) + -0.02125) = 0.1579515625 Calculate the square root of the right side: 0.397431205 Break this problem into two subproblems by setting ((b) + -0.02125) equal to 0.397431205 and -0.397431205.Subproblem 1
(b) + -0.02125 = 0.397431205 Simplifying (b) + -0.02125 = 0.397431205 b + -0.02125 = 0.397431205 Reorder the terms: -0.02125 + b = 0.397431205 Solving -0.02125 + b = 0.397431205 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.02125' to each side of the equation. -0.02125 + 0.02125 + b = 0.397431205 + 0.02125 Combine like terms: -0.02125 + 0.02125 = 0.00000 0.00000 + b = 0.397431205 + 0.02125 b = 0.397431205 + 0.02125 Combine like terms: 0.397431205 + 0.02125 = 0.418681205 b = 0.418681205 Simplifying b = 0.418681205Subproblem 2
(b) + -0.02125 = -0.397431205 Simplifying (b) + -0.02125 = -0.397431205 b + -0.02125 = -0.397431205 Reorder the terms: -0.02125 + b = -0.397431205 Solving -0.02125 + b = -0.397431205 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.02125' to each side of the equation. -0.02125 + 0.02125 + b = -0.397431205 + 0.02125 Combine like terms: -0.02125 + 0.02125 = 0.00000 0.00000 + b = -0.397431205 + 0.02125 b = -0.397431205 + 0.02125 Combine like terms: -0.397431205 + 0.02125 = -0.376181205 b = -0.376181205 Simplifying b = -0.376181205Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.418681205, -0.376181205}
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