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Simplifying -1b2 + -7b + 10 = 0 Reorder the terms: 10 + -7b + -1b2 = 0 Solving 10 + -7b + -1b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + 7b + b2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 7b + 10 + b2 = 0 + 10 Reorder the terms: -10 + 10 + 7b + b2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7b + b2 = 0 + 10 7b + b2 = 0 + 10 Combine like terms: 0 + 10 = 10 7b + b2 = 10 The b term is 7b. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7b + 12.25 + b2 = 10 + 12.25 Reorder the terms: 12.25 + 7b + b2 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + 7b + b2 = 22.25 Factor a perfect square on the left side: (b + 3.5)(b + 3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (b + 3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
b + 3.5 = 4.716990566 Simplifying b + 3.5 = 4.716990566 Reorder the terms: 3.5 + b = 4.716990566 Solving 3.5 + b = 4.716990566 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + b = 4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + b = 4.716990566 + -3.5 b = 4.716990566 + -3.5 Combine like terms: 4.716990566 + -3.5 = 1.216990566 b = 1.216990566 Simplifying b = 1.216990566Subproblem 2
b + 3.5 = -4.716990566 Simplifying b + 3.5 = -4.716990566 Reorder the terms: 3.5 + b = -4.716990566 Solving 3.5 + b = -4.716990566 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + b = -4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + b = -4.716990566 + -3.5 b = -4.716990566 + -3.5 Combine like terms: -4.716990566 + -3.5 = -8.216990566 b = -8.216990566 Simplifying b = -8.216990566Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.216990566, -8.216990566}
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