About math quadratic equation by factoring?

Question

hello everyone i have a problem...it is about math which is the topic is quadratic equation by factoring so i don't know what is the answer of this question

see here below..

4x2+19x-5=0 <---can you help me of this what is the answer and can you teach me step by step...

and also this question..

4x2-12a+5=0

49a2-70+25=0

can you help me about this because i don't know what is the correct answer of that math quadratic equation by factoring can you help me and please see you info or step by step on how you get the correct answer thanks

Answer 1

4x2+19x-5=0

ok firstly, 4 x 2 = 8

therefore, it is 8 + 19x -5

ok now, -5 +8 = 3.

so 19x + 3 = 0

put the on the other side therefore

19x = -3

x = -3/19

4x2-12a+5=0

49a2-70+25=0

ok, 8 - 12a + 5 = 0

-12a +13 = 0

-12a = -13

12a = 13

a = 12/13

and i do not understand

49a2-70+25=0

the 49a2?

Answer 2

1)

4x^2 + 19x - 5 = 0

4x^2 + 20x - x - 5 = 0

(4x^2 + 20x) - (x + 5) = 0

4x(x + 5) - 1(x + 5) = 0

(x + 5)(4x - 1) = 0

x + 5 = 0

x = -5

4x - 1 = 0

4x = 1

x = 1/4 (0.25)

∴ x = -5 , 1/4 (0.25)

= = = = = = = =

2)

4x^2 - 12x + 5 = 0

4x^2 - 2x - 10x + 5 = 0

(4x^2 - 2x) - (10x - 5) = 0

2x(2x - 1) - 5(2x - 1) = 0

(2x - 1)(2x - 5) = 0

2x - 1 = 0

2x = 1

x = 1/2 (0.5)

2x - 5 = 0

2x = 5

x = 5/2 (2.5)

∴ x = 1/2 (0.5) , 5/2 (2.5)

= = = = = = = =

3)

49a^2 - 70a + 25 = 0

49a^2 - 35a - 35a + 25 = 0

(49a^2 - 35a) - (35a - 25) = 0

7a(7a - 5) - 5(7a - 5) = 0

(7a - 5)(7a - 5) = 0

7a - 5 = 0

7a = 5

a = 5/7

∴ a = 5/7

Answer 3

First off - you will need to factor these equations via Quadratic Equation.

The Quadratic Equation is:

X = -B (+ or -) *square root sign* B squared - 4ac (OVER) 2a

              

If the equation above is too hard to understand than please check the link I supplied below - the first equation you read on the page will be the correct one that I tried to explain.

                                  @http://upload.wikimedia.org/math/3/e/a/3...

Basically - you want to break the equations that you supplied into sub-categories A, B, and C.

These are supplied to you right there in the equation in the following order.

Ax2-Ba+C=0 &lt;-- That is the order you will find the numbers in, so in this case A is 4, B is -12, and C is 5.

With this info, you will then want to plug it in via quadratic equation. Fill in the various A, B, and C&#039;s with the numbers that I have supplied above, and do the math. That will bring you to...

X=12+*square root of*144-88 (OVER) 8

Subtract that middle equating there...

X=12+*square root of* 56 (OVER) 8

56 is not a perfect square, therefore you will need to break it down in to it&#039;s multiples, and one of which MUST be a perfect square.

(Perfect Squares: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144... etc, basically any number times itself [2x2, 3x3, 4x4, 5x5, etc...] )

56 can be divided by the perfect square : 4.

So that will give you...

X=12+radical 14, radical 4 (OVER 8)

Now split up that radical 4, because it&#039;s a perfect square and change it into the number 2, as 2 is the square root of 4, it&#039;s simply just solving for square root, and bring it to the front of the equation by the 12.

X=12+2|Radical 14

------------------------------

               8

I&#039;m sure there&#039;s more, look on the website i supplied below it may be able to help you further, however it&#039;s quite confusing. That problem doesn&#039;t look very easy either. I may be doing it wrong.

Answer 4

For factoring, it can be done through this way:

4x^2 + 19x - 5 = 0

Multiply the coefficient of x^2 and the constant. That is 4 * (-5) = -20

Then find two numbers a and b which when multiplied is equal to -20 and when added is equal to coefficient of x, in this case, 19.

We find that a and b are 20 and -1 (by trial and error)

so the factors are (x-20) and (x-(-1)) or (x+1)

Add the coefficient of x^2 to each of the factor, become:

(4x-20) and (4x+1)

Then the complete factorization of  

4x^2 + 19x - 5 = 0 is

(4x-20)(4x+1)/4=0

(x-5)(4x+1) = 0 is the factorization.

Just do the same for the other to get the answer

(2x-5)(2x-1) = 0

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