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Simplifying 8b2 + -34b + 10 = -25 Reorder the terms: 10 + -34b + 8b2 = -25 Solving 10 + -34b + 8b2 = -25 Solving for variable 'b'. Reorder the terms: 10 + 25 + -34b + 8b2 = -25 + 25 Combine like terms: 10 + 25 = 35 35 + -34b + 8b2 = -25 + 25 Combine like terms: -25 + 25 = 0 35 + -34b + 8b2 = 0 Factor a trinomial. (7 + -4b)(5 + -2b) = 0Subproblem 1
Set the factor '(7 + -4b)' equal to zero and attempt to solve: Simplifying 7 + -4b = 0 Solving 7 + -4b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4b = 0 + -7 -4b = 0 + -7 Combine like terms: 0 + -7 = -7 -4b = -7 Divide each side by '-4'. b = 1.75 Simplifying b = 1.75Subproblem 2
Set the factor '(5 + -2b)' equal to zero and attempt to solve: Simplifying 5 + -2b = 0 Solving 5 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2b = 0 + -5 -2b = 0 + -5 Combine like terms: 0 + -5 = -5 -2b = -5 Divide each side by '-2'. b = 2.5 Simplifying b = 2.5Solution
b = {1.75, 2.5}
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