(x-1)^2=7x^2-9x-4=64x^2-8x+3=5I have to solve these by factoring……..?

Question

(x-1)^2=7
x^2-9x-4=6
4x^2-8x+3=5
I have to solve these by factoring……..? these are separate problems......do i find the root first...........

Answer 1

You have to get to set it equal to zero

1) expand the (x-1)^2 to x^2-2x+1
yes I was wrong with this look at the answer by physicspat which I believe is also not accurate
so here's the correct one x^2-2x+1=7 which by subtracting 7 from both side we get we get x^2-2x-6=0, which is not factor-able so quad equestion.

x = (2 +/- sqrt(4+24))/2 which is x= 1 +/- sqrt (7)

next one is
2) x^2-9x-4=6 which is x^2-9x-10=0 factoring gives (x-10)(x+1)=0
so the x= 10 or -1

and the last one is
3) 4x^2-8x+3=5 which is 4x^2-8x-2=0 (which if correct is not factor-able so use quadratic equestion for it)
the answer whould be x = (8 +/- sqrt( 64 + 32))/8 which is
x = (8 +/- sqrt( 96))/8 which can be writin as (2 +/- sqrt(6))/2

Answer 2

#1 You can find the root first, x-1 = +-sqrt 7 solve for the two values of x, x = 1 + sqrt 7, x = 1 - sqrt 7.
or
you can multiply it out first
x^2 - 2x + 1 = 7 ; x^2 - 2x - 6 = 0. This doesn't facor easily so you find the roots using quadratic formula.

#2 yeilds x^2 - 9x - 10 = (x - 10)(x + 1) = 0
x = 10, x = -1

#3 yields 4x^2 - 8x - 2 = 0 or 2x^2 - 4x - 1 = 0
Again, this doesn't factor over the rational numbers so lets do this one by completing the square

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

completing the square on the left
x^2 -2x + 1 = 1/2 + 1
(x-1)^2 = 3/2 = 6/4

x-1 = +- sqrt(6/4) = +-1/2 sqrt6
x = 1 + 1/2 sqrt6
x = 1 - 1/2 sqrt6

square roots in answers come from either the quadratic formula or completing the square. I suppose you could factor them but I've never seen anybody do it.

If the problem is to find the roots, factoring only works efficienly
if it factors fairly easily.

Answer 3

You first want to set one side equal to zero. (x-1)^2-7=0. Then, expand your squared binomial to get x^2-2x+1-7=0. Combine like terms and you have x^2-2x-6=0. I'm afraid you can't factor this one, so you have to use quadratic formula to find x (x = 1 + (square root of 7)/2 and 1 - (square root of 7)/2). Here is the work for the other two equations.

x^2-9x-4=6
x^2-9x-10=0
(x-10)*(x+1)=0
x = 10, -1

4x^2-8x+3=5
4x^2-8x-2=0
2x^2-4x-1=0
x = 1 + (square root of 6)/2 and 1 - (square root of 6)/2

Answer 4

3(x-2) + 2 = 9x -4 - 8x Distrubute the 3 , and combine like variables 3x -6 +2 = x -4 3x -4 = x - 4 then move the x's to one side 2x = 0 x = 0

Answer 5

dhaval70 shows the proper procedure, however, he did make a mistake on the first one.

That's actually beneficial since it just points out how important it is to do a double check of your answer once you're finished. Using FOIL for (x-3)(x+2), I get x^2 + 2x -3x -6, which is x^2 - x - 6. That doesn't match the x^2 - 2x - 6 that you have. The right answer is (x - 3.645)(x+1.645).

(I almost tend to think you have an error in the problem, since the answers are almost always kept to nice easy integer values when you're first learning factoring. I had to use a slide rule to get the answer and would have had a hard time coming up with those values just through trial and error.)

Edit: Duh! Use the quadratic equation for the first one as Pat said.

Answer 6

no u dont find the root at all i dont believe....x^2-9x-4=6.....I think you.........add 4 to both sides and then factor x^2-9x=10 . Now you have (x+3)(x-3)=10..then set your factors as problems....x+3=10 and x-3=10 Solve.Your answers are 7 and 13....I THINK

Answer 7

(x - 1)^2 = 7
(x - 1)(x - 1) = 7
x^2 - x - x + 1 = 7
x^2 - 2x - 6 = 0
This can't be factored

so

x = (-b ± sqrt(b^2 - 4ac))/2a
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-6))/(2(1))
x = (2 ± sqrt(4 + 24))/2
x = (2 ± sqrt(28))/2
x = (2 ± sqrt(4 * 7))/2
x = (2 ± 2sqrt(7))/2
x = 1 ± sqrt(7)

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

x^2 - 9x - 4 = 6
x^2 - 9x - 10 = 0
(x - 10)(x + 1) = 0
x = 10 or -1

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

4x^2 - 8x + 3 = 5
4x^2 - 8x - 2 = 0
2(2x^2 - 4x - 1) = 0

this can't be factored

x = (-(-4) ± sqrt((-4)^2 - 4(2)(-1)))/(2(2))
x = (4 ± sqrt(16 + 8))/4
x = (4 ± sqrt(24))/4
x = (4 ± sqrt(4 * 6))/4
x = (4 ± 2sqrt(6))/4
x = (1/2)(2 ± sqrt(6))