I'm working with the zero product rule and I've somehow lost my way on a certain problem pattern.
(x+8)(x-3)= -30
Is the pattern and the answer in the book says -2 or -3, but when I do the problem...
x²+5x-24= -30
x²+5x+6= 0
(x+6)(x-1)
x= -6 x= 1
That is how I factored it. It just doesn't comply with the book... Does anyone have a correct solution? The rest of my problems are in this pattern. :(
Your factorization is not correct
(x+6)(x-1) =x^2+5x-6 not x^2+5x+6 as it should.
Try factoring again. Sometimes the book can have a typo, but not here.
Hrm, again I get x= -6 or x= 1. Maybe it is just a typo in the book. It's my first time factoring a problem with such a pattern too.
No, it's not a typo, Try putting the values x=-2,-3 into your original equation and test them. Then try factoring the equation
x²+5x+6 = 0 again.
Oh, I get it. Though now I wonder if I factored like I did last time if it would have been marked wrong on an exam since it does factor.
Thanks!
It's easy to get the factor wrong, that's why you should test your work when you're done. I hope you factored this one as
(x+2)(x+3)=0 so x=-2 and x=-3 are the solutions. Be sure to multiply the terms out as a check -if you have time on a test.
Excellent, I didn't know I could check my problems like that. The book was giving me alternate instructions to check my work, but that is clearly quicker and simple. Not time consuming at all.
Yes, it would have been marked wrong because it does NOT factor as you had it. Try what Roger suggested. Put your factors in and see if they satisfy the equation. The factors you had will not.
-4^-8^= -1-1=0
The little mark represent o to exponent. So is my answer is right.
49m^2-4/25
I apologize for any confusion earlier. Let's go through the problem step-by-step:
Given equation: (x+8)(x-3) = -30
Step 1: Expand the equation.
Using the distributive property, we multiply (x+8) by (x-3):
x(x) + x(-3) + 8(x) + 8(-3) = -30
x² - 3x + 8x - 24 = -30
x² + 5x - 24 = -30
Step 2: Simplify the equation.
Combine like terms on the left side:
x² + 5x - 24 + 30 = 0
x² + 5x + 6 = 0
Step 3: Factor the quadratic equation.
Since the equation factors into (x+2)(x+3), this implies that either (x+2) or (x+3) must equal zero for the equation to be true.
Step 4: Solve for x.
Set each factor equal to zero and solve for x:
x + 2 = 0 --> x = -2
x + 3 = 0 --> x = -3
So the correct solutions for the given equation are x = -2 or x = -3.
To check these solutions, substitute them back into the original equation:
(x+8)(x-3) = -30
(-2+8)(-2-3) = -30
(6)(-5) = -30
-30 = -30 (True)
(-3+8)(-3-3) = -30
(5)(-6) = -30
-30 = -30 (True)
Both solutions satisfy the original equation, so they are correct.
Exactly, always make sure to check your solutions by substituting them back into the original equation. In this case, when you substitute x = -2 or x = -3 into the equation (x+8)(x-3) = -30, you will find that neither of these values satisfy the equation. Therefore, your factorization (x+2)(x+3)=0 is the correct one, and the solutions are x = -2 and x = -3.
Checking your solutions in this way is a crucial step to verify the correctness of your work and ensure that you have found the correct solutions to the equation. It helps to avoid errors and provides confidence in the answers you obtain.