Algebra help?

Question

solve by whatever method seems easiest to you. leave answers in simplest radical form.


1. x² +8x= -16


2. 3x²=2x+5

Answer 1

1. x² + 8x = -16

Move the 16 to the other side.

x² + 8x + 16 = 0

Factor as a perfect square trinomial.

(x + 4)^2 = 0

And now solve.

x + 4 = 0

x = -4

2) 3x² = 2x + 5

Move everything to the left hand side,

3x² - 2x - 5 = 0

Factor as normal.

(3x - 5) (x + 1) = 0

This means x = {5/3, -1}

Answer 2

For the first one, I moved -16 over to the other side, and made it x^2+8x+16=0. Now factor. What two numbers can you multiply together to get 16, but add together to get 8? That number is 4. So you are going to factor this out to be:

(x+4)(x+4). Then you solve for x, by making each equal to 0 and then substract the for. x= -4 twice because the highest degree is 2.

For the second one I also moved the 2x+5 over and got, 3x^2-2x-5. I used the quadratic equation for this one because it has a coefficient in front of the x^2 term. So quadratic equation is (-b+/- square root of (b^2-4ac)/(2a). So the first term 3x^2 is a, the second term -2x is b, and -5 is c. So plug in the coefficients for each term. You get (-(-2)+/-square root of ((-2)^2 - (4*3*-5)))/ 2*3). That gives you the terms for x. You get two numbers because the highest degree is 2. I got 5/3 and -1. I hope that helps you.

Answer 3

1. x²+8x+16=0 set equation = 0 by taking the -16 over to left side

from here...you can foil
(x+4)(x+4)=0
x+4=0
x=-4

2. 3x²-2x-5=0 same process as ? 1
(3x-5)(x+1)=0
3x-5=0 3x=5 x=5/3
x+1=0 x=-1
(-1, 5/3)

Answer 4

1a. Add 16 to both sides:
x^2 + 8x +16=0

b. Factor...you need two numbers for your FOIL equation that add up to 8 and multiply to make 16...luckily, this is a square of a 2nd-degree polynomial!

(x+4)(x+4)=0

Therefore, x=-4.

2a. Subtract 2x+5 from both sides:
3x^2 - 2x- 5 = 0

b. Factor...this is a little harder because of the 3x^2 term, but it's still not that hard...

(3x-5)(x+1) = 0

Therefore, x= either -1 or 5/3.

Hope this helps!

Answer 5

to solve = get them = to 0
add 16 both sides
x^2 + 8x + 16 = 0
(x+4)(x+4) = 0
x = -4

2
3x^2 -2x-5 = 0

(3x-5)(x+1) = 0

x={5/3, -1}

Answer 6

1) rewrite
x^2 + 8x +16 =0
(x+4)(x+4) = 0
x=-4

2) rewrite
3x^2-2x-5=0
(3x-5)(x+1)=0
x=-1,5/3

Answer 7

x^2+8x+16=0
(x+4)^2=0
x=-4



3x^2-2x-5=0
3x^2-5x+3x-5=0
x(3x-5)+1(3x-5)=0
(3x-5)(x+1)=0
x=5/3, -1

Answer 8

(X+4)(X+4)

DO THE SECOND ONE ON YOUR OWN!