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Simplifying 14b2 + -24b + -24 = -8 + 7b2 Reorder the terms: -24 + -24b + 14b2 = -8 + 7b2 Solving -24 + -24b + 14b2 = -8 + 7b2 Solving for variable 'b'. Reorder the terms: -24 + 8 + -24b + 14b2 + -7b2 = -8 + 7b2 + 8 + -7b2 Combine like terms: -24 + 8 = -16 -16 + -24b + 14b2 + -7b2 = -8 + 7b2 + 8 + -7b2 Combine like terms: 14b2 + -7b2 = 7b2 -16 + -24b + 7b2 = -8 + 7b2 + 8 + -7b2 Reorder the terms: -16 + -24b + 7b2 = -8 + 8 + 7b2 + -7b2 Combine like terms: -8 + 8 = 0 -16 + -24b + 7b2 = 0 + 7b2 + -7b2 -16 + -24b + 7b2 = 7b2 + -7b2 Combine like terms: 7b2 + -7b2 = 0 -16 + -24b + 7b2 = 0 Factor a trinomial. (-4 + -7b)(4 + -1b) = 0Subproblem 1
Set the factor '(-4 + -7b)' equal to zero and attempt to solve: Simplifying -4 + -7b = 0 Solving -4 + -7b = 0 Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -7b = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7b = 0 + 4 -7b = 0 + 4 Combine like terms: 0 + 4 = 4 -7b = 4 Divide each side by '-7'. b = -0.5714285714 Simplifying b = -0.5714285714Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4Solution
b = {-0.5714285714, 4}
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