!!Quadratic equation facilitate please!!?
Question: I have the equation:
(x2 / (0.1- x)) = 6.94 x 10-4
could somebody please comfort me solve x, using the quadratic formula (+ workings please)
(In the above example x2= x squared)
THanks!
Answers:
(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 paw side,
x^2 = [6.94 x 10^(-5)] - [6.94 x 10^(-4)]x
Move everything to the left foot 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 proven 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 subtract that.
(6.94 x 10-4)
this part here confuses me.
is it 6.94x or is it ultimately 69.4 - 4?
please clarify.
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
( using your notations )
(x2 / (0.1- x)) = 6.94 x 10-4
multiplyh both sides next to
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
very jammy..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
I have the equation:
(x^2 / (0.1- x)) = 6.94 * 10^(-4)
could somebody please back me solve x, using the quadratic formula (+ workings please)
So
x^2 = 6.94 * 10^(-4)(0.1 - x)
ie x^2 + 6.94 * 10^(-4) x - 6.94 * 10^(-5) = 0
Using the formula
x = 1/2 (-6.94 * 10^(-4) ± √[(6.94 * 10^(-4))^2 - 4*1*(-6.94 * 10^(-5)])
≈ 1/2 (-6.94 * 10^(-4) ± 0.0166757799)
≈0.007991, -0.008685
ie 7.991 x 10^(-3), -8.685 x 10^(-3)
(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 share you but right now I hold to go out, sorry! bye
healthy new year!
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)
as a result, x=7.99089*10^(-3)or
-8.68489*10^(-3)
i hope that this helps
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
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