solve the equation by factoring 3x^2-8x-3=0
(3x+1)(1x-3)=0
Now solve each for zero:
3x+1=0
and
1x-3=0
Lance can you help me.?
Certainly! I'd be happy to help you solve the equation 3x^2 - 8x - 3 = 0 using factoring.
To begin factoring, we need to find two numbers that multiply to -9 (the product of the leading coefficient, 3, and the constant term, -3) and add up to -8 (the coefficient of the x term, -8).
To achieve this, we can write the middle term -8x as the sum of two terms that multiply to -9x and add up to -8x. The factors of -9 that satisfy this condition are -9 and +1. Therefore, we can rewrite the equation as:
3x^2 - 9x + x - 3 = 0
Next, we group the terms by pairs:
(3x^2 - 9x) + (x - 3) = 0
Now, we factor out the Greatest Common Factor (GCF) from each group:
3x(x - 3) + 1(x - 3) = 0
Notice that we now have a common binomial factor, (x - 3), which we can factor out:
(3x + 1)(x - 3) = 0
This means that either (3x + 1) equals zero or (x - 3) equals zero. We can set up two separate equations to solve for x:
3x + 1 = 0 OR x - 3 = 0
To solve the first equation, we isolate x by subtracting 1 from both sides:
3x = -1
Then, we divide both sides by 3:
x = -1/3
For the second equation, we isolate x by adding 3 to both sides:
x = 3
Therefore, the solutions to the equation 3x^2 - 8x - 3 = 0 are x = -1/3 and x = 3.