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Simplifying 5b2 + 3b + -26 = -6 Reorder the terms: -26 + 3b + 5b2 = -6 Solving -26 + 3b + 5b2 = -6 Solving for variable 'b'. Reorder the terms: -26 + 6 + 3b + 5b2 = -6 + 6 Combine like terms: -26 + 6 = -20 -20 + 3b + 5b2 = -6 + 6 Combine like terms: -6 + 6 = 0 -20 + 3b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 0.6b + b2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.6b + 4 + b2 = 0 + 4 Reorder the terms: -4 + 4 + 0.6b + b2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.6b + b2 = 0 + 4 0.6b + b2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.6b + b2 = 4 The b term is 0.6b. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6b + 0.09 + b2 = 4 + 0.09 Reorder the terms: 0.09 + 0.6b + b2 = 4 + 0.09 Combine like terms: 4 + 0.09 = 4.09 0.09 + 0.6b + b2 = 4.09 Factor a perfect square on the left side: (b + 0.3)(b + 0.3) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (b + 0.3) equal to 2.022374842 and -2.022374842.Subproblem 1
b + 0.3 = 2.022374842 Simplifying b + 0.3 = 2.022374842 Reorder the terms: 0.3 + b = 2.022374842 Solving 0.3 + b = 2.022374842 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + b = 2.022374842 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + b = 2.022374842 + -0.3 b = 2.022374842 + -0.3 Combine like terms: 2.022374842 + -0.3 = 1.722374842 b = 1.722374842 Simplifying b = 1.722374842Subproblem 2
b + 0.3 = -2.022374842 Simplifying b + 0.3 = -2.022374842 Reorder the terms: 0.3 + b = -2.022374842 Solving 0.3 + b = -2.022374842 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + b = -2.022374842 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + b = -2.022374842 + -0.3 b = -2.022374842 + -0.3 Combine like terms: -2.022374842 + -0.3 = -2.322374842 b = -2.322374842 Simplifying b = -2.322374842Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.722374842, -2.322374842}
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