algebra - factoring/quadratic equation?

Question

7. 2x2 - 4x + 1 = 0
8. 3x2 + 2x = 7
9. x2 + 8x + 9 = -7

Answer 1

7. 2x^2 - 4x + 1 = 0
not factorable
a = 2, b = -4, c = 1
x = [ -(-4) +or- sqrt((-4)^2 - 4(2)(1)) ] / (2(2))
x = [ 4 +or- sqrt(8) ] / 4
x = [ 4 + 2sqrt(2) ] / 4 or x = [ 4 - 2sqrt(2) ] / 4
x = [2 + sqrt(2) ] / 2 or x = [ 2 - sqrt(2) ] / 2

8. 3x^2 + 2x = 7
3x^2 + 2x - 7 = 0
not factorable
a = 3, b = 2, c = -7
x = [ -2 +or- sqrt(2^2 - 4(3)(-7) ] / (2(3))
x = [ -2 +or- sqrt(88) ] / 6
x = [ -2 + 2sqrt(22) ] / 6 or [ -2 - sqrt(22) ] / 6
x = [ -1 + sqrt(22) ] / 3 or x = [ -1 - sqrt(22) ] / 3

9. x^2 + 8x + 9 = -7
x^2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
x + 4 = 0
x = -4

Answer 2

The quadratic equation is easier to use when you're not dealing with whole numbers, and have access to a scientific calculator. it's :
[-b+ or - the sqrt(b^2- 4*a*c)]/(2*a)
where a is the number in front of x^2, b is in front of x, and c is the number without an x.
As a side note, you have to set the equations equal to 0 before you can solve using the quadratic.

Answer 3

7.2x2 - 4x + 1 = 0
=(2x-1)^2 = 0
2x-1 = 0 --> x =1/2 (double root)

8.3x2 + 2x = 7
3x^2 +2x-7= 0
x= [-2 +/- sqrt(2^2+4*3*7)]/(2*3)
x = [-2 +/- 2sqrt(22)]/(6)
x = -1/3 +/- 1/3 sqrt(22)

9.x2 + 8x + 9 = -7
x^2 +8x +16 = 0
(x+4)^2 = 0
x+4 = 0
x= -4 <-- double root

Answer 4

7. 2x^2-4x+1=0
It is impossible to factor this out, so we use the quadratic formula.
[ 4+/-(16-8)^1/2 ]/4
( 4+/-3sqrt2 )/4
8. 3x^2+2x-7=0
Use quadratic formula again
( -2+/-(4+84)^1/2 )/6
I'm sure you can solve for it from there.
9. x^2+8x+16=0
(x+4)^2=0
x=-4

Answer 5

hi :) x^2 - 10 = 0 => x^2 = 10 => x = ±?10 x^2 - 2x + a million = 0 => (x - a million)(x - a million) = 0 (in view that (x - a million)^2 = x^2 - 2x + a million) => x = a million, a million x^2 - 7x + 10 x^2 - 5x - 2x + 10 x(x - 5) - 2(x - 5) (x - 2)(x - 5) 5n^3 + 20n^2 + 15n 5n(n^2 + 4n + 3) 5n(n^2 + n + 3n + 3) 5n[n(n + a million) + 3(n + a million)] 5n[(n +a million)(n + 3)] 5n(n + a million)(n + 3) 81x^4 + 3x 3x(27x^3 + a million) 3x[(9x)^3 + a million^3] 3x(3x + a million)(9x^2 - 3x + a million) desire it facilitates :)