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Simplifying 10b2 + -2b + -14 = 0 Reorder the terms: -14 + -2b + 10b2 = 0 Solving -14 + -2b + 10b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -1b + 5b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1b + 5b2)' equal to zero and attempt to solve: Simplifying -7 + -1b + 5b2 = 0 Solving -7 + -1b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.2b + b2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.2b + 1.4 + b2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.2b + b2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.2b + b2 = 0 + 1.4 -0.2b + b2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.2b + b2 = 1.4 The b term is -0.2b. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2b + 0.01 + b2 = 1.4 + 0.01 Reorder the terms: 0.01 + -0.2b + b2 = 1.4 + 0.01 Combine like terms: 1.4 + 0.01 = 1.41 0.01 + -0.2b + b2 = 1.41 Factor a perfect square on the left side: (b + -0.1)(b + -0.1) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (b + -0.1) equal to 1.187434209 and -1.187434209.Subproblem 1
b + -0.1 = 1.187434209 Simplifying b + -0.1 = 1.187434209 Reorder the terms: -0.1 + b = 1.187434209 Solving -0.1 + b = 1.187434209 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + b = 1.187434209 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + b = 1.187434209 + 0.1 b = 1.187434209 + 0.1 Combine like terms: 1.187434209 + 0.1 = 1.287434209 b = 1.287434209 Simplifying b = 1.287434209Subproblem 2
b + -0.1 = -1.187434209 Simplifying b + -0.1 = -1.187434209 Reorder the terms: -0.1 + b = -1.187434209 Solving -0.1 + b = -1.187434209 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + b = -1.187434209 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + b = -1.187434209 + 0.1 b = -1.187434209 + 0.1 Combine like terms: -1.187434209 + 0.1 = -1.087434209 b = -1.087434209 Simplifying b = -1.087434209Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.287434209, -1.087434209}Solution
b = {1.287434209, -1.087434209}
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