I have no clue how to do this helppppppop
3x^2 - 23x - 8 = 0
3x^2 - 24x + x - 8 = 0
3x(x - 8) + 1(x - 8) = 0
(3x + 1)(x - 8) = 0
x = -1/3 or x = 8
3x² - 23x - 8 = 0
(3x+1)(x-8) = 0
3x+1 = 0 ⇒ x = -⅓
x-8 = 0 ⇒ x = 8
So the solution is
x = -⅓ or x = 8.....................ANS
Ax^2 + Bx + C = 0
Find two numbers that add up to -23(B) and multiply to -24(AC):
-24 and +1
Rewrite the middle term as sum of -24x + x:
From here, we factor it by grouping:
3x(x - 8) + (x - 8) = 0
(x - 8)(3x + 1) = 0
x = -1/3, 8
The trick is to find a pair a, b that add to give -23 and multiply to give 3*-8 = -24, that is the coefficient of x² times the constant.
With that, we obtain a = -24, b = 1
Now we split the -23x into two parts, so:
3x² - 24x + x - 8 = 0
Then we factor the first and last two terms:
Now we see that both have a factor of (x - 8), so we factor that out:
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Answers & Comments
3x^2 - 23x - 8 = 0
3x^2 - 24x + x - 8 = 0
3x(x - 8) + 1(x - 8) = 0
(3x + 1)(x - 8) = 0
x = -1/3 or x = 8
3x² - 23x - 8 = 0
(3x+1)(x-8) = 0
3x+1 = 0 ⇒ x = -⅓
x-8 = 0 ⇒ x = 8
So the solution is
x = -⅓ or x = 8.....................ANS
Ax^2 + Bx + C = 0
Find two numbers that add up to -23(B) and multiply to -24(AC):
-24 and +1
Rewrite the middle term as sum of -24x + x:
3x^2 - 24x + x - 8 = 0
From here, we factor it by grouping:
3x(x - 8) + (x - 8) = 0
(x - 8)(3x + 1) = 0
x = -1/3, 8
The trick is to find a pair a, b that add to give -23 and multiply to give 3*-8 = -24, that is the coefficient of x² times the constant.
With that, we obtain a = -24, b = 1
Now we split the -23x into two parts, so:
3x² - 24x + x - 8 = 0
Then we factor the first and last two terms:
3x(x - 8) + (x - 8) = 0
Now we see that both have a factor of (x - 8), so we factor that out:
(3x + 1)(x - 8) = 0