Solve by factoring.
a) x^2 + 3x - 28 = 0
(x+7)(x-4)
d)x^2 + 8x + 16 = 0
(x+4)(x+4)
f)9x^2 - 4 = 0
i)8k^2 - 3k = 0
k)x^2/6 - x + 4/3 = 0
did i do a and d right? Can you show me how to solve the rest?
a) If (x+7)(x-4) = 0 then x = -7 or 4.
d) x = -4
Yes, you did a and d right, but carry it out all the way.
f) (3x-2)(3x+2) = 0
I don't have the time to deal with the remaining problems.
Yes, you have solved (a) and (d) correctly. Let's solve the remaining equations.
f) To solve 9x^2 - 4 = 0 by factoring, you want to rewrite the equation in the form (x + a)(x + b) = 0, where a and b are numbers that, when multiplied, give you the constant term (-4), and when added, give you the coefficient of the x term (0 in this case).
In 9x^2 - 4 = 0, the coefficient of x^2 is 9, which tells us that the equation can be factored into two binomials. The constant term is -4.
To find the factors of -4, we need to consider pairs of numbers that multiply to -4. The pairs that satisfy this are (1, -4) and (-1, 4). Now we need to check which pair also satisfies the condition of adding up to 0, which is (1, -4).
Therefore, we can rewrite the equation as (3x + 2)(3x - 2) = 0.
i) To solve 8k^2 - 3k = 0 by factoring, we want to rewrite it as k*(ax + b) = 0, where a and b are constants that we need to determine.
First, observe that k is a common factor on the left side. We can factor it out to get k(8k - 3) = 0.
Now we solve each factor individually:
Case 1: k = 0
This means one of the solutions is k = 0.
Case 2: 8k - 3 = 0
To solve 8k - 3 = 0, we add 3 to both sides: 8k = 3. Then divide by 8: k = 3/8. This gives us another solution.
Therefore, the complete solution is k = 0 or k = 3/8.
k) To solve x^2/6 - x + 4/3 = 0 by factoring, we want to rewrite the equation in the form (x + a)(x + b) = 0.
To start, let's get rid of the fraction by multiplying every term in the equation by the least common multiple (LCM) of the denominators, which is 6. Multiplying by 6 gives us:
6(x^2/6) - 6x + 6(4/3) = 0
x^2 - 6x + 8 = 0
Now we need to factor x^2 - 6x + 8. We need two numbers that multiply to 8 and add up to -6. The numbers -2 and -4 satisfy this condition.
Therefore, the factored form is (x - 2)(x - 4) = 0.
I hope this helps! Let me know if you have any further questions.