Factor the expression.
9b^2+48b+46
To factor the expression 9b^2 + 48b + 46, we can use the quadratic formula:
b = (-b ± √(b^2 - 4ac))/(2a)
For this expression, a = 9, b = 48, and c = 46. Plugging these values into the formula, we get:
b = (-(48) ± √((48)^2 - 4(9)(46)))/(2(9))
Simplifying further:
b = (-48 ± √(2304 - 1656))/18
b = (-48 ± √648)/18
b = (-48 ± √36 * 18)/18
b = (-48 ± 6√18)/18
b = -8 ± (√18)/3
So the factors of the expression are:
(3b + (-8 + √18)/3)(3b + (-8 - √18)/3)