To solve the quadratic equation [tex]\(9b^2 + 30b + 25 = 0\)[/tex], we will use the quadratic formula which is given by:
[tex]\[ b = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A} \][/tex]
For the quadratic equation [tex]\(Ax^2 + Bx + C = 0\)[/tex], the coefficients are:
[tex]\( A = 9 \)[/tex]
[tex]\( B = 30 \)[/tex]
[tex]\( C = 25 \)[/tex]
Substituting these values into the quadratic formula:
[tex]\[ b = \frac{-30 \pm \sqrt{30^2 - 4 \cdot 9 \cdot 25}}{2 \cdot 9} \][/tex]
First, calculate the discriminant:
[tex]\[ 30^2 - 4 \cdot 9 \cdot 25 = 900 - 900 = 0 \][/tex]
Since the discriminant is zero, there is exactly one real solution.
Now compute the value of [tex]\( b \)[/tex]:
[tex]\[ b = \frac{-30 \pm \sqrt{0}}{18} \][/tex]
[tex]\[ b = \frac{-30 \pm 0}{18} \][/tex]
[tex]\[ b = \frac{-30}{18} \][/tex]
[tex]\[ b = -\frac{5}{3} \][/tex]
Therefore, the solution to the equation [tex]\(9b^2 + 30b + 25 = 0\)[/tex] is:
[tex]\[ b = -\frac{5}{3} \][/tex]
Hence, the best answer is:
A. [tex]\( b = -\frac{5}{3} \)[/tex]
