The exact solution?

Question

Say i have:

5x-3=6

Now if I'm trying to find the exact solution would I try and get x alone so that the answer would be:

X=9/5

And what about
4(y-2)=10y+5

or

(2x-5)(x+8)=0

or

x^2-2x-8=0

or

8x^2-24=0

Answer 1

yes, the first one is right. "Exact" solution means to leave it in fractional form... Don't calculate what 9/5 is in decimals. (Although in this case, 9/5 is a terminating decimal, so it doesn't matter...)

4(y-2) = 10y + 5
4y - 8 = 10y + 5
-6y - 8 = 5
-6y = 13
y = -13/6

In this case, you would need to leave it as a fraction because the decimal is 2.16666 (with a repeating 6).

(2x-5)(x + 8) = 0
set each piece =0 and solve:
2x - 5 = 0
x = 5/2
and
x + 8 = 0
x = -8

x^2 - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4, -2

8x^2 - 24 = 0
8x^2 = 24
x^2 = 3
x = (sqrt 3) and (- sqrt 3)

Answer 2

4y - 8 = 10y + 5
-6y = 13
y = 13/6

(2x - 5)(x + 8) = 0 has two solutions.
Either 2x - 5 = 0 (x = 5/2)
or x + 8 = 0 (x = -8)

x^2 - 2x - 8 = 0 is solved using the quadratic formula.
Given the equation ax^2 + bx + c = 0,
x = (-b +/- sqrt(b^2 - 4 * a * c)) / (2 * a)

Here, x = (2 +/- sqrt(4 + 32))/(2 * 2)
x = (2 +/- sqrt(36))/4
x = (2 +/- 6)/4
x = 8/4 or -4/4
x = 2 or -1

8x^2 = 24
x^2 = 3
x = +/- sqrt(3)

Answer 3

4(y-2)=10y+5
=>8y-8=10y+5
=>8y-10y=5+8
=> -2y=13
=>y=13/-2= -6.5
(2x-5)(x+8)=0
As the product of the two factors is zero,at least one of them must be zero
Therefore either 2x-5=0 or x+8=0
If 2x-5=0,then 2x=5 or x=5/2 or 2.5
If x+8=0,then x= -8
Hence x=2.5 or -8 ans
x^2-2x-8=0
=>x^2-4x+2x-8=0
=>x(x-4)+2(x-4)=0
=>(x-4)(x+2)=0
Therefore either x-4=0 or x+2=0
Hence x=4 or -2 ans
8x^2-24=0
=>8x^2=24
=> x^2=24/8=3
=>x= +/- sqrt 3 ans

Answer 4

4(y - 2) = 10y + 5
4y - 8 = 10y + 5
-8 = 6y + 5
-13 = 6y
y = -13/6

(2x - 5)(x + 8) = 0
2x - 5 = 0 x + 8 = 0
2x = 5 x = -8
x = 5/2
x = 5/2 , -8

x^2 - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4, -2

8x^2 - 24 = 0
8x^2 = 24
x^2 = 3
x = +/- sqrt (3)

Answer 5

4(y-2)=10y+5
4y - 8 = 10y + 5
6y = -13
y = -13/6

(2x-5)(x+8)=0
2x - 5 = 0
x = 5/2
or
x + 8 = 0
x = -8

x^2-2x-8=0
(x - 4)(x + 2) = 0
x = 4
or
x = -2

8x^2-24=0
x^2 = 3
x = sqrt(3)

Answer 6

because of the fact the quantity is a hundred and twenty and the top of the field is 3, the part of the backside of the field is 40. There for the climate of the sq. base are the sq. root of 40. upload returned the 6 inches removed from the two facet and you have the unique dimensions.