!!!!Quadratic equation help please!!!!?

Question

I have the equation:

(x2 / (0.1- x)) = 6.94 x 10-4

could somebody please help me solve x, using the quadratic formula (+ workings please)

(In the above example x2= x squared)

THanks!

hello

its 6.94 times 10 to the power of minus 4

great stuff, thank you all and happy new year,

the positive answer in needed was 7.99 x 10^-3

Answer 1

(x^2) / (0.1 - x) = (6.94 x 10^(-4))

Your first step would be to multiply both sides of the equation by (0.1 - x)

x^2 = (6.94 x 10^(-4)) (0.1 - x)

Now, convert the 0.1 to scientific notation.

x^2 = (6.94 x 10^(-4)) ([1.0 x 10^(-1)] - x)

Expand the right hand side,

x^2 = [6.94 x 10^(-5)] - [6.94 x 10^(-4)]x

Move everything to the left hand side,

x^2 + [6.94 x 10^(-4)]x - [6.94 x 10^(-5)] = 0

Now, we're going to get rid of those annoying scientific notation things and multiply everything by 10^(5) (or 100000)

100000x^2 + 6.94(10)x - 6.94 = 0
100000x^2 + 69.4x - 6.94 = 0

At this point, we use the quadratic formula.

x = [-69.4 +/- sqrt ( [69.4]^2 - 4(100000)(6.94) )] / (200000)

x = [-69.4 +/- sqrt ( [2780816.36] ) ] / (200000)

x = {-3.47 x 10^(-4)} +/- sqrt [2780816.36]/200000

I'll leave it up to you to calculate that.

Answer 2

(x2/(0.1-x) = 6.94 * 10-4 CROSS MULTIPLICATION

x2 = 6.94 * 10-4 ( 0.1 -x )
x2 = 6.94 * 10-5 - 6.94 * 10-4x
x2 + 6.94 * 10-4x - 6.94 * 10-5 = 0

from here onwards do the normal factorisation

man this is tough...I will try to do it and tell you but right now I have to go out, sorry! bye
happy new year!

Answer 3

( using your notations )
(x2 / (0.1- x)) = 6.94 x 10-4

multiplyh both sides with
0.1 - x

x2 = 6.94 x 10-4 x (0.1- x)

equals
x2 - 6.94 x 10-4 x (0.1- x) = 0

x2 - 0.694 x 10-4 + 6.94 x 10-4 x x = 0

x_one = ( -6.94 x 10-4 + sqrt ( 6.94 x 10-8 + 4x0.694 x 10-4 ) ) / 2
x_two= ( -6.94 x 10-4 -sqrt ( 6.94 x 10-8 + 4x0.694 x 10-4 ) ) / 2

Answer 4

One basic time era that looks regularly is "equations." for many, that could be a buzz word it fairly is recognizable as a math time era yet extremely understanding the time era might sometime get away people. the two maximum basic equations are linear equations and quadratic equations yet, of direction, purely giving an equation a recognition does not inevitably clarify what that is. So, a clearer definition of what precisely the two maximum basic equations - linear and quadratic equations - is needed. A linear equation refers to a definite equation it fairly is graphed on a straight away line. additionally, a linear equation possesses on the line one variable it fairly is often talked approximately as "X" and "X" will consistently be of a level it fairly is a million at maximum. (it fairly is, there are actually not any exponents; yet once you're searching for exponents then wait and see because of the fact we can get to them presently!) an easy occasion of a linear equation may be 1x + 2 = 3. for sure, x might equivalent a million throughout this actual occasion and that is found out by technique of purely using somewhat algebra on the equation to come to a decision X. 3 minus 2 equals a million. subsequently, X might desire to equivalent one as a million x a million equals one. And, nope, not all linear equations are that straightforward as they arrive as complicated as 6(x + 3) = 24 (x +0), however the easy ingredient of putting apart x to locate the answer would not substitute. A quadratic equation is barely diverse from a linear equation in one admire: extra than a number of of the figures is squared. (The word quadratic derives from the Latin word for squared) the easy variety of a quadratic equation is ax2 + bx + c = 11. In certainly one of those equation, if a = a million, b = 2 and c = 3 then X might desire to equivalent 2. all of us be attentive to this because of the fact 2 squared is 4 and four x a million = 4. 2 x 2 = 4. As with a linear equation, there could be extra complicated variations of a quadratic equation yet purely with the easy and sophisticated linear equations hardship-unfastened algebraic operations can yield the main suitable answer.

Answer 5

the solution is:
x^2 / (0.1-x) = 6.94 x 10^-4
Cross multiplying
10^4 x x^2 = 6.94 (0.1 - x)
10^4x^2 + 6.94x - 0.694 = 0

ax^2 +bx +c = 0 can be factorized as
a(x - [-b+{(b^2 - 4ac)^1/2}/2a}] (x - [-b-{(b^2 - 4ac)^1/2}/2a}]

OR
x = [-b+ {(b^2 - 4ac)^1/2}/2a}]
x = [-b - {(b^2 - 4ac)^1/2}/2a}]

(b^2 - 4ac)^1/2 = (6.94^2 - 4x10^4x.694)^1/2
= (-27711.84)^1/2

** (b^2 - 4ac)^1/2 = 166.47i

x = (-6.94 + 166.47i)/(2x10^4) or (-6.94 - 166.47i)/(2x10^4)
x = (-3.47 + 83.23i)/10^4 or -(3.47 - 83.23i)/10^4

Hence
x = (83.23 - 3.47i) / 10^4 or
x = -(-83.23 +3.47i) / 10^4

Answer 6

I have the equation:

(x² / (0.1- x)) = 6.94 * 10^(-4)

could somebody please help me solve x, using the quadratic formula (+ workings please)
So
x² = 6.94 * 10^(-4)(0.1 - x)

ie x² + 6.94 * 10^(-4) x - 6.94 * 10^(-5) = 0

Using the formula

x = ½(-6.94 * 10^(-4) ± √[(6.94 * 10^(-4))² - 4*1*(-6.94 * 10^(-5)])

≈ ½(-6.94 * 10^(-4) ± 0.0166757799)

≈0.007991, -0.008685

ie 7.991 x 10^(-3), -8.685 x 10^(-3)

Answer 7

very easy..hihi
x^2 / (0.1-x) = 6.94 x 10^-4
Cross multiplying
10^4 x x^2 = 6.94 (0.1 - x)
10^4x^2 + 6.94x - 0.694 = 0

ax^2 +bx +c = 0 can be factorized as
a(x - [-b+{(b^2 - 4ac)^1/2}/2a}] (x - [-b-{(b^2 - 4ac)^1/2}/2a}]

OR
x = [-b+ {(b^2 - 4ac)^1/2}/2a}]
x = [-b - {(b^2 - 4ac)^1/2}/2a}]

(b^2 - 4ac)^1/2 = (6.94^2 - 4x10^4x.694)^1/2
= (-27711.84)^1/2

** (b^2 - 4ac)^1/2 = 166.47i

x = (-6.94 + 166.47i)/(2x10^4) or (-6.94 - 166.47i)/(2x10^4)
x = (-3.47 + 83.23i)/10^4 or (-3.47 - 83.23i)/10^4

Hence
x = (83.23 - 3.47i) / 10^4 or
x = -(83.23 +3.47i) / 10^4

Answer 8

(6.94 x 10-4)
this part here confuses me.

is it 6.94x or is it ultimately 69.4 - 4?

please clarify.

Answer 9

x^2/(0.1-x)=6.94*10^(-4)
x^2=6.94*10^(-4)(0.1-x)
multply through by 10^4
10,000x^2=0.694-6.94x
10,000x^2+6.94x-0.694=0
using the quadratic formula
[x={-b+/-sqrt(b^2-4ac)}/2a]
2a=2*10,000=20,000
-b=-6.94
b^2=6.94^2=48.1636
-4ac=-(4*10,000*(-0.694)
=27,760
sqrt{b^2-4ac}=
sqrt{48.1636+27,760}
=166.757792
{-b+or-sqrt(b^2-4ac)}/2a
={-6.49+sqrt(48.1636+27,760)}
/20,000
={-6.94+or-166.7577992}
/20,000
=7.99089*10^(-3)or
-8.68489*10^(-3)

therefore, x=7.99089*10^(-3)or
-8.68489*10^(-3)

i hope that this helps

Answer 10

Cross multiply and move everything to one side.
x^2 = (6.94E-4)(0.1) - (6.94E-4)x
x^2 + (6.94E-4)x - 6.94E-5 = 0
Here apply the quadratic formula.
x = 0.00799 or x = -0.00868