To solve the quadratic equation 84x^2 + 16x = 0 by factoring out the greatest common factor (GCF), first, let's find the GCF of the coefficients 84 and 16.
The prime factorization of 84 is 2^2 * 3 * 7, and the prime factorization of 16 is 2^4.
The common factors are 2^2 = 4.
Now, let's factor out the GCF from the equation:
4(21x^2 + 4x) = 0
Now, we have a quadratic equation of the form ax^2 + bx = 0, where a = 21 and b = 4.
To solve this equation, we can set each factor equal to zero:
4 = 0 (This cannot be true)
21x^2 + 4x = 0
By factoring the quadratic equation further, we can now solve for x:
x(21x + 4) = 0
Setting each factor equal to zero:
x = 0
21x + 4 = 0
Solving the linear equation:
21x = -4
x = -4/21
Therefore, the solutions to the quadratic equation 84x^2 + 16x = 0, factored by the GCF, are x = 0 and x = -4/21.
Solve the quadratic equation 84x^2+16x=0
by factoring out the GCF.
1 answer