What am I doing wrong? Quadratic equations, solve for x?

Question

1) 4x^2 - 2x - 2x + 1 = 0
(4x^2 - 2x) - (2x +1) = 0
what do I do from here?

2) 1/7x^2 = 3/7x


3) 5x^2 = 11x - 2
5x^2 - 11x + 2 = 0
(5x^2 - 10x) - (x + 2)
What do I do?

If you could answer with explanations, please, thank you very much.

Answer 1

1)4x^2-2x-2x+1=0
Combine the middle terms:
4x^2-4x+1=0
(2x-1)(2x-1)=0
x=1/2

2)1/7x^2=3/7x
Multiply both sides by 7:
x^2=3x
Subtract 3x from both sides:
x^2-3x=0
Factor out an x:
x(x-3)=0
x=0 and 3

3)5x^2=11x-2
Subtract 11x and add 2 from both sides:
5x^2-11x+2=0
(5x-1)(x-2)=0
x=1/5 and 2

Answer 2

1) 4x^2 - 2x - 2x +1 = 0
4x^2 - 4x +1 = 0
(2x - 1) (2x - 1) = 0 (becos of (a-b)^2 = a^2 - 2ab + b^2)
=> 2x = 1
x = 1/2

2) Do u mean this:
(1/7)x^2 = (3/7)x
(multiply by 7 throughout to cancel the common denominator): x^2 = 3x
=> x^2 - 3x = 0
x(x-3)=0
x=0 or x=3

or u meant this:
1/(7x^2) = 3/(7x)
(cross-multiple): 3*(7x^2) = 1*(7x)
21x^2 -7x = 0
7x(3x-1) = 0
x=0 or 3x=1
=> x=0 or x=1/3

3) 5x^2 = 11x - 2
5x^2 - 11x + 2 =0
(By factorisation): (5x-1)(x-2)=0
5x-1 =0 or x-2=0
5x =1 or x=2
x=1/5 or x=2

Everytime after you've brought all the terms to 1 side of the equation, it will mean that it's time to do factorisation.

For factorization, u may use the formula x=(-B+or-[sqrt (B^2-4AC)]/2A where Ax^2+Bx+C=0.

Please take a look at my source, if you are not sure how to do factorization.

Remember to check ur factorization by expanding the brackets out again to ensure u did ur factorization correctly :)

Answer 3

1) 4x^2 - 2x - 2x + 1 = 0

You didn't properly factor (-1) out of the last two terms. You also didn't factor the greatest common monomial from the first two terms.

Factor the first two terms and the last two terms.

2x(2x - 1) - (2x - 1) = 0
{Note: Factoring a minus is the same as factoring (-1).}
Group them. Factor (2x - 1) out of the whole equation.

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

Therefore,

2x - 1 = 0
2x = 1
x = 1/2

Your second question is ambiguous so I will not attempt to answer it.

3) 5x^2 = 11x - 2
5x^2 - 11x + 2 = 0

Split -11x into -10x and -x, like you have done.

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

Factor the same way it was done above.

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

Therefore,
x - 2 = 0
5x - 1 = 0

x = {2, 1/5}

Answer 4

1) 4x^2 - 2x - 2x +1 = 0
4x^2 - 4x +1 = 0
(2x - 1)(2x - 1) = 0
x = 1/2

2)1/7x^2 - 3/7x = 0
7(1/7x^2 - 3/7x) = 0(7)
x^2 - 3x = 0
x (x - 3) = 0
x = 0 ; x = 3

3) 5x^2 = 11x - 2
5x^2 - 11x + 2 =0
(5x - 1) (x - 2) = 0
5x - 1 = 0 ; x - 2 = 0
x=1/5 ; x = 2

Answer 5

OK...I don't get it ... Why you ,the Americans ,always want to do things the harder way ?...

Like this :
3) 5x^2 = 11x - 2
5x^2 - 11x + 2 = 0
(5x^2 - 10x) - (x + 2)

it's much easier that way :

5x^2 = 11x - 2
5x^2 - 11x + 2 = 0

D = b^2 - 4ac
D = 11^2 - 4.5.2
D = 121 - 4.10
D = 121 - 40
D = 81

x = -b + D^-2 / 2a = 11 + 9 /2.5 = 20/10 = 2
x = -b - D^-2 /2a = 11 - 9 /2.5 = 2/10 = 1/5

Isn't that much easier !?

Ohh..And the answer above are correct... I don't think that I have to write the same thing again...
Good luck with the Maths :-D

Answer 6

1.
The grouping you have written does not appear useful to me. Let's start again:
4x^2 - 2x - 2x + 1 = 0
Combine the x terms:
4x^2 - 4x + 1 = 0
Factorise:
(2x - 1)^2 = 0
Equate each factor 2x - 1 separately to 0 to get your answers.
As both factors are the same, you have only one answer (unless you choose to regard it as two equal answers).
2x - 1 = 0
Add 1:
2x = 1
Divide by 2:
x = 1/2.

2.
1/(7x^2) = 3/(7x)
Multiply by 7x^2:
1 = 3x
x = 1/3.

Maybe you meant:
(1/7)x^2 = (3/7)x
Then multiply by 7:
x^2 = 3x
Subtract 3x:
x^2 - 3x = 0
Factorise:
x(x - 3) = 0
Equate each factor separately to 0:
x = 0 or x - 3 = 0
In the second case, add 3:
x = 0 or x = 3.

3.
5x^2 = 11x - 2
Subtract 11x and add 2:
5x^2 - 11x + 2 = 0
Factorise:
(5x - 1)(x - 2) = 0
Equate each factor separately to 0:

Either
5x - 1 = 0
Add 1:
5x = 1
Divide by 5:
x = 1/5

or
x - 2 = 0
Add 2:
x = 2.

Answer 7

1) 4x^2 - 2x - 2x + 1 = 0
(4x^2 - 2x) - (2x +1) = 0
- (2x + 1) is incorrect.
(4x^2 - 2x) - (2x -1) = 0
2x(2x - 1) - 1(2x -1) = 0
(2x - 1)(2x - 1) = 0
x = 1/2

2) 1/7x^2 = 3/7x is ambiguous.
(1/7)x^2 = (3/7)x
x^2 = 3x
x^2 - 3x = 0
x(x - 3) = 0
x = 0,3

1/(7x^2) = 3/(7x)
21x^2 = 7x
21x^2 - 7x = 0
7x(3x - 1) = 0
x = 0,1/3

3) 5x^2 = 11x - 2
5x^2 - 11x + 2 = 0
(5x^2 - 10x) - (x + 2)
You have the same error here as in 1)
(5x^2 - 10x) - (x - 2) = 0
5x(x - 2) - 1(x - 2) = 0
(5x - 1)(x - 2) = 0
x = 1/5,2

Answer 8

4x^2 - 2x - 2x + 1 = 0

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

(2x - 1)^2 = 0

2x - 1 = 0 ===> x = 1/2

2) 1/7x^2 = 3/7x

1/7x(x -3) = 0

x=0 or x=3

3) 5x^2 = 11x - 2

5x^2 - 11x + 2 = 0

(5x^2 - 10x) - (x - 2) =0 (you keep getting your signs mixed up)

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

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

x = 1/5 or x=2

Answer 9

4x²n - 2x - 2x + 1 = 0

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

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

- - - - - - - -
1/7x² = 3/7x

7x(1/7x²) = 7x(3/7x)

x = 3

- - - - - -

5x² = - 11x - 2

5x² + 11x = - 11x - 2 + 11x

5x² + 11x = - 2

5x² + 11x + 2 = - 2 + 2

5x² + 11x + 2 = 0

5x² + 10x + x + 2 = 0

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

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

- - - - - - - s-

Answer 10

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