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Simplifying 60b2 + -168b + -10 = 0 Reorder the terms: -10 + -168b + 60b2 = 0 Solving -10 + -168b + 60b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -84b + 30b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -84b + 30b2)' equal to zero and attempt to solve: Simplifying -5 + -84b + 30b2 = 0 Solving -5 + -84b + 30b2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.1666666667 + -2.8b + b2 = 0.0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -2.8b + 0.1666666667 + b2 = 0.0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -2.8b + b2 = 0.0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -2.8b + b2 = 0.0 + 0.1666666667 -2.8b + b2 = 0.0 + 0.1666666667 Combine like terms: 0.0 + 0.1666666667 = 0.1666666667 -2.8b + b2 = 0.1666666667 The b term is -2.8b. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8b + 1.96 + b2 = 0.1666666667 + 1.96 Reorder the terms: 1.96 + -2.8b + b2 = 0.1666666667 + 1.96 Combine like terms: 0.1666666667 + 1.96 = 2.1266666667 1.96 + -2.8b + b2 = 2.1266666667 Factor a perfect square on the left side: (b + -1.4)(b + -1.4) = 2.1266666667 Calculate the square root of the right side: 1.458309524 Break this problem into two subproblems by setting (b + -1.4) equal to 1.458309524 and -1.458309524.Subproblem 1
b + -1.4 = 1.458309524 Simplifying b + -1.4 = 1.458309524 Reorder the terms: -1.4 + b = 1.458309524 Solving -1.4 + b = 1.458309524 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + b = 1.458309524 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + b = 1.458309524 + 1.4 b = 1.458309524 + 1.4 Combine like terms: 1.458309524 + 1.4 = 2.858309524 b = 2.858309524 Simplifying b = 2.858309524Subproblem 2
b + -1.4 = -1.458309524 Simplifying b + -1.4 = -1.458309524 Reorder the terms: -1.4 + b = -1.458309524 Solving -1.4 + b = -1.458309524 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + b = -1.458309524 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + b = -1.458309524 + 1.4 b = -1.458309524 + 1.4 Combine like terms: -1.458309524 + 1.4 = -0.058309524 b = -0.058309524 Simplifying b = -0.058309524Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.858309524, -0.058309524}Solution
b = {2.858309524, -0.058309524}
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