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Simplifying 10b2 + -3b + -35 = 0 Reorder the terms: -35 + -3b + 10b2 = 0 Solving -35 + -3b + 10b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.5 + -0.3b + b2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.3b + 3.5 + b2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.3b + b2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.3b + b2 = 0 + 3.5 -0.3b + b2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.3b + b2 = 3.5 The b term is -0.3b. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3b + 0.0225 + b2 = 3.5 + 0.0225 Reorder the terms: 0.0225 + -0.3b + b2 = 3.5 + 0.0225 Combine like terms: 3.5 + 0.0225 = 3.5225 0.0225 + -0.3b + b2 = 3.5225 Factor a perfect square on the left side: (b + -0.15)(b + -0.15) = 3.5225 Calculate the square root of the right side: 1.876832438 Break this problem into two subproblems by setting (b + -0.15) equal to 1.876832438 and -1.876832438.Subproblem 1
b + -0.15 = 1.876832438 Simplifying b + -0.15 = 1.876832438 Reorder the terms: -0.15 + b = 1.876832438 Solving -0.15 + b = 1.876832438 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + b = 1.876832438 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + b = 1.876832438 + 0.15 b = 1.876832438 + 0.15 Combine like terms: 1.876832438 + 0.15 = 2.026832438 b = 2.026832438 Simplifying b = 2.026832438Subproblem 2
b + -0.15 = -1.876832438 Simplifying b + -0.15 = -1.876832438 Reorder the terms: -0.15 + b = -1.876832438 Solving -0.15 + b = -1.876832438 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + b = -1.876832438 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + b = -1.876832438 + 0.15 b = -1.876832438 + 0.15 Combine like terms: -1.876832438 + 0.15 = -1.726832438 b = -1.726832438 Simplifying b = -1.726832438Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.026832438, -1.726832438}
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