can someone help me i've tried different numbers but i can come out to factor this:
2b^2+6b-216=0
why don't you divide the equation by 2 to get b^2+3b-108=0
now by trial and error, can you find two factors of 108 that have a difference of 3?
(b-9)(2b+24)
To factor the quadratic equation 2b^2 + 6b - 216 = 0, we can apply the factoring method. However, before doing that, let's simplify the equation first.
You suggested dividing the equation by 2 to simplify it, which is a good approach. Dividing every term by 2, we get:
(b^2 + 3b - 108) = 0
Now, we can focus on factoring the simplified equation, b^2 + 3b - 108 = 0. To factor this, we need to find two numbers that multiply to -108 and add up to 3.
To do this, we can list all the factors of 108:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Now, we look for two numbers that have a difference of 3. From the list above, we find that 9 and -12 satisfy this condition since 9 - (-12) = 21.
Next, we can write the factors of the quadratic equation as:
(b - 9)(b + 12) = 0
So, the factored form of the quadratic equation 2b^2 + 6b - 216 = 0 is:
(b - 9)(b + 12) = 0