Solve using Quadratic Formula

2x^2-(1/2)x-(3/2)=0

Can someone please show me a step by step solution to solving this using the quadratic formula. I'm having trouble incorporating the fractions into it.

Hello,

2x² – (½)x – (3/2) = 0

If you are troubled with fractions, just get rid of it! Multiply the whole equation by 2 !
2x² – (½)x – (3/2) = 0
4x² – x – 3 = 0

Then apply quadratic formula:
4x² – x – 3 = 0
a=4 b=-1 c=-3

Discriminant ∆ = b² – 4ac = (-1)² – 4×4×(-3) = 1 + 48 = 49 = 7²

Thus the roots:
x₁ = (-b – √∆)/(2a) = [-(-1) – 7]/(2×4) = -6/8 = -¾
x₂ = (-b + √∆)/(2a) = [-(-1) + 7]/(2×4) = 8/8 = 1

= = = = == = = = = = = = = == = = = = = =
Now if you insist on using the fractions:

2x² – (½)x – (3/2) = 0
a=2 b=-½ c=-3/2

Discriminant ∆ = b² – 4ac = (-½)² – 4×2×(-3/2) = ¼ + 12 = 49/4 = (7/2)²

Thus the roots:
x₁ = (-b – √∆)/(2a) = [-(-½) – (7/2)]/(2×2) = (½ – 7/2)/4 = -6/8 = -¾
x₂ = (-b + √∆)/(2a) = [-(-½) + (7/2)]/(2×2) = (½ + 7/2)/4 = 8/8 = 1

Regards,
Dragon.Jade :-)

2x^2-(1/2)x-(3/2)=0 get rid of the fractions - multiply all by 2
4x^2 -x - 3=0 factor - how do you get the product 4?
(2x - )(2x + )
or
(4x + ) (x - )
what factors will give you the product -3? -1,3 or 1,-3
puzzle - where can you put these pairs in the brackets to get a product
of -3 and a SUM of -1 ?
(4x + 3 ) (x - 1 ) = 0
2 solutions
(4x + 3 ) = 0

or (x - 1 ) = 0

take it from there

Make things a bit easier by removing the fractions.

Multiplying by 2 we get:

4x² - x - 3 = 0

=> (4x + 3)(x - 1) = 0

i.e. x = -3/4 or x = 1

Using the formula we get:

x = {1 ± √[(-1)² - 4(4)(-3)]}/8

=> x = [1 ± √(1 + 48)]/8

=> x = (1 ± √49)/8

i.e. x = (1 ± 7)/8

so, x = -3/4 or 1 as before.

:)>

Simplify the expression...

2^(2x) * 2^(-1) - 3 * 2^x * 2^(-1) + 1 = 0
2^(2x)/2 - 3 * 2^(x)/2 + 1 = 0

Multiply each term by 2 to get:

2^(2x) - 3 * 2^(x) + 2 = 0

Let u = 2^x. This gives us:

(2^x)² - 3(2^x) + 2 = 0
u² - 3u + 2 = 0

Factoring..

(u - 2)(u - 1) = 0

By zero-product property:

u - 2 = 0 and u - 1 = 0
u = 2 and u = 1

Finally, since u = 2^x..

2^x = 2 and 2^x = 1
x = 1 and x = 0

x = [0.5+-sqrt(0.5^2 + 4*2*3/2)]/4

x = [0.5+-sqrt(12.25)]/4