Before we can factor the equation, let's convert first it into a general form of a quadratic equation ax² + bx + c = 0 where "x" is a variable. See the steps below.
Subtract 8b² and 2 on both sides of the equation.
[tex]23b^2-49b+26-8b^2-2=8b^2+2-8b^2-2[/tex]Arrange the terms in terms of their degree.
[tex]23b^2-8b^2-49b+26-2=8b^2-8b^2+2-2[/tex]Combine similar terms.
[tex]15b^2-49b+24=0[/tex]We have converted the equation into its general form and that is 15b² - 49b + 24 = 0.
Let's now factor this equation using the Slide and Divide Method.
1. Slide the leading coefficient 15 to the constant term 24 by multiplying them.
[tex]15\times24=360[/tex]Upon sliding, the equation now becomes:
[tex]b^2-49b+360=0[/tex]2. Let's find the factors of 360 that sums up to -49.
• 6 and 60 → sum is 66
,• 8 and 45 → sum is 53
,• 9 and 40 → sum is 49
,• -9 and -40 → sum is -49
Therefore, the factors of 360 that sums to -49 are -9 and -40.
Hence, the equation b² - 49b + 360 can be factored into:
[tex](b-9)(b-40)=0[/tex]3. Since we slide 15 earlier, divide the factors -9 and -40 by 15 by simplifying the fraction.
[tex]-\frac{9}{15}\Rightarrow-\frac{9\div3}{15\div3}=-\frac{3}{5}[/tex][tex]-\frac{40}{15}\Rightarrow-\frac{40\div5}{15\div5}=-\frac{8}{3}[/tex]4. To find the factors of the equation, simply slide the denominator in each factor to b.
[tex]\begin{gathered} (b-\frac{3}{5})\Rightarrow(5b-3) \\ (b-\frac{8}{3})\Rightarrow(3b-8) \end{gathered}[/tex]The factors of the equation are (5b - 3)(3b - 8).
Let's now solve for b. Simply equate each factor to zero and solve for b.
[tex]\begin{gathered} 5b-3=0 \\ 5b=3 \\ b=\frac{3}{5} \end{gathered}[/tex][tex]\begin{gathered} 3b-8=0 \\ 3b=8 \\ b=\frac{8}{3} \end{gathered}[/tex]ANSWER:
The factors of the equation are (5b - 3)(3b - 8) and the values of b are 3/5 and 8/3.
