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Simplifying 5b2 + -2b + -14 = 0 Reorder the terms: -14 + -2b + 5b2 = 0 Solving -14 + -2b + 5b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -0.4b + b2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -0.4b + 2.8 + b2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -0.4b + b2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -0.4b + b2 = 0 + 2.8 -0.4b + b2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -0.4b + b2 = 2.8 The b term is -0.4b. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4b + 0.04 + b2 = 2.8 + 0.04 Reorder the terms: 0.04 + -0.4b + b2 = 2.8 + 0.04 Combine like terms: 2.8 + 0.04 = 2.84 0.04 + -0.4b + b2 = 2.84 Factor a perfect square on the left side: (b + -0.2)(b + -0.2) = 2.84 Calculate the square root of the right side: 1.685229955 Break this problem into two subproblems by setting (b + -0.2) equal to 1.685229955 and -1.685229955.Subproblem 1
b + -0.2 = 1.685229955 Simplifying b + -0.2 = 1.685229955 Reorder the terms: -0.2 + b = 1.685229955 Solving -0.2 + b = 1.685229955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + b = 1.685229955 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + b = 1.685229955 + 0.2 b = 1.685229955 + 0.2 Combine like terms: 1.685229955 + 0.2 = 1.885229955 b = 1.885229955 Simplifying b = 1.885229955Subproblem 2
b + -0.2 = -1.685229955 Simplifying b + -0.2 = -1.685229955 Reorder the terms: -0.2 + b = -1.685229955 Solving -0.2 + b = -1.685229955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + b = -1.685229955 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + b = -1.685229955 + 0.2 b = -1.685229955 + 0.2 Combine like terms: -1.685229955 + 0.2 = -1.485229955 b = -1.485229955 Simplifying b = -1.485229955Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.885229955, -1.485229955}
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