having a hard time with a couple of problems please help
(3x+5)^2+8=0
also
6-9=12 divided by y+5 y-5 y^2-25
On the first, two ways...
Let me do the easiest. Notice that the first term for real x will always be positive, and the second term is positive, the sum is zero. So there are no real x.
(3x+5)^2=-8
take the square root of each side..
3x+5=sqrt (-8)= 2i sqrt2
then solve for x. It will be a complex number.
Second
Multiply both sides by (y^2-25)
6(y-5)-9(y+5)=12
multiply out, gather terms and solve for y.
Thank you very much
Sure, I can help you with those problems!
Let's start with the first one:
(3x+5)^2 + 8 = 0
To solve this equation, we need to isolate the variable (x) by getting rid of the square. We'll do that step by step:
1. Expand the square. (a+b)^2 = a^2 + 2ab + b^2
(3x+5)^2 = (3x)^2 + 2(3x)(5) + 5^2
= 9x^2 + 30x + 25
So, our equation becomes:
9x^2 + 30x + 25 + 8 = 0
2. Combine like terms:
9x^2 + 30x + 33 = 0
Now, we have a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it using factoring, completing the square, or the quadratic formula. In this case, factoring will work:
3. Factor the quadratic equation:
9x^2 + 30x + 33 = 0
(3x + 3)(3x + 11) = 0
Setting each factor equal to zero gives us two equations to solve:
3x + 3 = 0 or 3x + 11 = 0
4. Solve for x:
For the first equation, subtract 3 from both sides:
3x = -3
x = -1
For the second equation, subtract 11 from both sides:
3x = -11
x = -11/3
So, the solutions to the equation (3x+5)^2 + 8 = 0 are x = -1 and x = -11/3.
Now, let's move on to the second problem:
6 - 9 = (12)/(y+5)(y-5)(y^2-25)
To simplify this equation, we'll break it down step by step:
1. Simplify the expression on the right side:
(y + 5)(y - 5) = y^2 - 25
Now the equation becomes:
6 - 9 = 12/(y^2 - 25)
2. Solve the right side of the equation:
12/(y^2 - 25) = -3
3. Multiply both sides by (y^2 - 25) to get rid of the fraction:
12 = -3(y^2 - 25)
4. Distribute -3 on the right side:
12 = -3y^2 + 75
5. Move all terms to one side of the equation:
0 = -3y^2 + 75 - 12
= -3y^2 + 63
6. Divide both sides by -3 to isolate y^2:
0 = y^2 - 21
7. Take the square root of both sides:
y = ±√(21)
So, the solutions to the equation 6 - 9 = 12/(y+5)(y-5)(y^2-25) are y = √(21) and y = -√(21).
I hope this helps! Let me know if you have any further questions.