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Simplifying (5b + 4) + -2b(b + -5) = 7 Reorder the terms: (4 + 5b) + -2b(b + -5) = 7 Remove parenthesis around (4 + 5b) 4 + 5b + -2b(b + -5) = 7 Reorder the terms: 4 + 5b + -2b(-5 + b) = 7 4 + 5b + (-5 * -2b + b * -2b) = 7 4 + 5b + (10b + -2b2) = 7 Combine like terms: 5b + 10b = 15b 4 + 15b + -2b2 = 7 Solving 4 + 15b + -2b2 = 7 Solving for variable 'b'. Reorder the terms: 4 + -7 + 15b + -2b2 = 7 + -7 Combine like terms: 4 + -7 = -3 -3 + 15b + -2b2 = 7 + -7 Combine like terms: 7 + -7 = 0 -3 + 15b + -2b2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -7.5b + b2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -7.5b + -1.5 + b2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -7.5b + b2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -7.5b + b2 = 0 + -1.5 -7.5b + b2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -7.5b + b2 = -1.5 The b term is -7.5b. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5b + 14.0625 + b2 = -1.5 + 14.0625 Reorder the terms: 14.0625 + -7.5b + b2 = -1.5 + 14.0625 Combine like terms: -1.5 + 14.0625 = 12.5625 14.0625 + -7.5b + b2 = 12.5625 Factor a perfect square on the left side: (b + -3.75)(b + -3.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (b + -3.75) equal to 3.54436172 and -3.54436172.Subproblem 1
b + -3.75 = 3.54436172 Simplifying b + -3.75 = 3.54436172 Reorder the terms: -3.75 + b = 3.54436172 Solving -3.75 + b = 3.54436172 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + b = 3.54436172 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + b = 3.54436172 + 3.75 b = 3.54436172 + 3.75 Combine like terms: 3.54436172 + 3.75 = 7.29436172 b = 7.29436172 Simplifying b = 7.29436172Subproblem 2
b + -3.75 = -3.54436172 Simplifying b + -3.75 = -3.54436172 Reorder the terms: -3.75 + b = -3.54436172 Solving -3.75 + b = -3.54436172 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + b = -3.54436172 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + b = -3.54436172 + 3.75 b = -3.54436172 + 3.75 Combine like terms: -3.54436172 + 3.75 = 0.20563828 b = 0.20563828 Simplifying b = 0.20563828Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.29436172, 0.20563828}
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