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Simplifying 14b2 + -38b + -10 = 0 Reorder the terms: -10 + -38b + 14b2 = 0 Solving -10 + -38b + 14b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -19b + 7b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -19b + 7b2)' equal to zero and attempt to solve: Simplifying -5 + -19b + 7b2 = 0 Solving -5 + -19b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -2.714285714b + b2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -2.714285714b + 0.7142857143 + b2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -2.714285714b + b2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -2.714285714b + b2 = 0 + 0.7142857143 -2.714285714b + b2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -2.714285714b + b2 = 0.7142857143 The b term is -2.714285714b. Take half its coefficient (-1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. -2.714285714b + 1.841836734 + b2 = 0.7142857143 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714b + b2 = 0.7142857143 + 1.841836734 Combine like terms: 0.7142857143 + 1.841836734 = 2.5561224483 1.841836734 + -2.714285714b + b2 = 2.5561224483 Factor a perfect square on the left side: (b + -1.357142857)(b + -1.357142857) = 2.5561224483 Calculate the square root of the right side: 1.598787806 Break this problem into two subproblems by setting (b + -1.357142857) equal to 1.598787806 and -1.598787806.Subproblem 1
b + -1.357142857 = 1.598787806 Simplifying b + -1.357142857 = 1.598787806 Reorder the terms: -1.357142857 + b = 1.598787806 Solving -1.357142857 + b = 1.598787806 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + b = 1.598787806 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + b = 1.598787806 + 1.357142857 b = 1.598787806 + 1.357142857 Combine like terms: 1.598787806 + 1.357142857 = 2.955930663 b = 2.955930663 Simplifying b = 2.955930663Subproblem 2
b + -1.357142857 = -1.598787806 Simplifying b + -1.357142857 = -1.598787806 Reorder the terms: -1.357142857 + b = -1.598787806 Solving -1.357142857 + b = -1.598787806 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + b = -1.598787806 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + b = -1.598787806 + 1.357142857 b = -1.598787806 + 1.357142857 Combine like terms: -1.598787806 + 1.357142857 = -0.241644949 b = -0.241644949 Simplifying b = -0.241644949Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.955930663, -0.241644949}Solution
b = {2.955930663, -0.241644949}
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