Algebra 1 Help?

Question

I have two questions i need help with

1.x2 + 2x - 15 = 0

a. Solve by factoring.
b. Solve using the quadratic formula.

2.x2 + 4x - 21 = 0

a. Solve by factoring.
b. Solve using the quadratic formula.

Answer 1

x² + 2x - 15 = 0

x² - 3x + 5x - 15 = 0

Group factor

(x² - 3x) + (5x - 15) = 0

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

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

- - - - - - - - -s-

Answer 2

1. x^2 + 2x - 15 = 0

By factoring:
x^2 + 2x + 1 - 1 - 15 = 0

(x + 1)^2 - 16 = 0
(x + 1)^2 - 4^2 = 0
(x + 1 - 4)(x + 1 + 4) = 0
(x - 3)(x + 5) =0
x1=3 x2= -5

By formula
x1,2 = (-2 +- sqrt(2^2 + 4*15))/2 =
= (-2 +- sqrt(64))/2 = (-2 +- 8)/2 = -1 +- 4
x1 = -1+4 = 3
x2 = -1-4 = 5

2. By factoring:
x^2 +4x - 21 = 0

x^2 + 2*2x + 2^2 - 2^2 - 21=0
(x + 2)^2 - 4 - 21 = 0
(x + 2)^2 - 25 = 0

(x + 2)^2 - 5^2=0
(x + 2 - 5)(x + 2 + 5) = 0
(x - 3)(x + 7) = 0

x1=3
x2 = -7

By formula:
x1,2 = (-4 +- sqrt(4^2 + 4*21))/2 =
= [-4 +- sqrt(16 + 84)]/2 = [-4 +- sqrt(100)]/2 =
= (-4 +- 10)/2 = -2 +- 5
x1 = -2 + 5 = 3
x2 = -2 - 5 = -7

Answer 3

1.x2 + 2x - 15 = 0
=> (x+5)(x-3)
=> x=-5 OR x =3

Quadratic Formula

x = - b ± √ (b² - 4ac) / 2a
a= 1 , b=2 , c -15

2.x2 + 4x - 21 = 0
=>(x+7)(x-3)
=>x = -7 OR x= 3

Quadratic Formula

x = - b ± √ (b² - 4ac) / 2a
a=1 ,b= 4 , c= -21

Answer 4

Both problems are similiar.
In your first problem, you need to find 2 numbers that multiply together to make -15 but also add together to make 2. To get 2 numbers to mulitply together to make a negative number, one has to be postitive and the other has to be negative. To solve by using the quadratic formula, you just plug the values in a = 1, b = 2, and c = -15. You should already have the formula which is too complex to type in here.

In your second problem, you need to find 2 numbers that multiply together to make -21 but also add together to make 4. Again, one of those numbers will be positive and one will be negative because of the nature of mulitplication.

Answer 5

solve by factoring
x2+2x-15=0
x2+4x-21=0

-(x2+2x-15)=0 step 1
x2+4x-21=0

-x2-2x+15=0 step 2
x2+4x-21=0

2x-6=0 step 3
2x=6 step 4
x=3 answer

Answer 6

By Factoring:
x^2 + 2x - 15 = 0
=(x+5)(x-3)
Roots:
x=-5, x=3

Quadratic Equation:
x^2 + 2x - 15 = 0

-(2) +/- √(2)^2-4(1)(-15)
x=--------------------------------
2(1)

-2 +/- √4+60
x=-----------------
2

-2+/- √64
x=------------
2

-2+/-8
x=----------
2
Roots:
x= -2+8 x=-2-8
--------- --------
2 2
x = 3 x = -5



By Factoring:
x^2 + 4x - 21 = 0
= (x+7)(x-3)
Roots:
x=-7, x=3

Quadratic Equation
x^2+4x-21=0

x= -(4)+/-√(4)^2-4(1)(-21)
---------------------------------
2(1)
x= -4+/-√16+84
--------------------
2
x=-4+/-√100
-------------
2
x= -4+/-10
-------------
2
x=-2+/-5

Roots:
x= -2-5 x=-2+5
x= -7 x= +3




i hope you understand it

Answer 7

1.
a. (x-3)(x+5)=0
b. x= (-2)- {and for the second option use +} square root [(-2)^2-4*1*(-15) and then divide that on 2*1.

You will get 2 answers( because of 2 signs: + and -):
x=3 and x=-5

2.a. (x-3)(x+7)=0

Answer 8

1. x = 3 3/4

2. x = 3 1/2

Answer 9

1) (a)x^2+2x-15=0
or x^2-3x+5x-15=0
or x(x-3)+5(x-3)=0
(x-3)(x+5)=0
so either x=3 or x=-5 ans
(b) x=[-b+-sq rt{b^2-4ac}]/2a
=[-2+-sq rt{4-4.1.(-15)}]/2
=[-2+- sq rt{4+60}]/2
={-2+-sqrt(64)}/2
={-2+-8}/2
or =(-2+8)/2 or (-2-8)/2
or x=6/2=3 or x=-10/2=-5 ans
similarly you can solve the 2nd one.

Answer 10

The answer is 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.1