4x^2-4x-5=0?

Question

Solve the following equation for by using the quadratic formula:
4x^2-4x-5=0

x=

(If there is more than one solution, separate them with commas.)

there cannot be an "x" in the solution for x
yet the algebrator will not solve for x

Answer 1

Hello dear

4x^2-4x-5=0

● Step 1
if F(y) = ax^2 + bx + c
∆ = b^2 - 4(a)(c) & ∆ ≥ 0
F(x) = 4x^2-4x-5
a = +4 , b = -4 , c = -5
∆ = (-4^2) - 4 (4)(- 5)
∆ = 16 + 80
∆ = 96 ≥ 0

● Step 2
x = [ -b ± √ ∆ ] / 2a
{ √ 96 = √ (16 * 6 ) = 4 √ 6 )
x1 = [ -b + √ ∆ ] / 2a = [ -(-4) + 4 √ 6 ] / 2(4) = [ 4/8] + [ 4 √ 6 / 8 ]
x1 = 1/2 + 1/2 √ 6 = 1/2( 1 + √ 6)

x2 = [ -b - √ ∆ ] / 2a = [ -(-4) - 4 √ 6 ] / 2(4) = [ 4/8] - [ 4 √ 6 / 8 ]
x2 = 1/2 - 1/2 √ 6 = 1/2( 1- √ 6)
so
x 1 = -0.724745
x 2 = 1.72474

Good Luck Darling ♣

Answer 2

4x^2 - 4x - 5 = 0
is of the form ax^2 + bx + c
where a = 4, b = -4 and c = -5

Plugging these into x = [-b ± sqrt(b^2 - 4ac)] / (2a) gives :

x = {-(-4) ± sqrt[(-4)^2 - 4(4)(-5)} / (2 * 4)

= [4 ± sqrt(16 +16 * 5)] / 8

= [4 ± sqrt(16 * 6)] / 8

= [4 ± 4 * sqrt(6)] / 8

= [1 ± sqrt(6)] / 2

The 2 solutions are : [1 - sqrt(6)] / 2 , [1 + sqrt(6)] / 2

Answer 3

Do you know the quadratic formula?

All you do is plug in 4 for a, -4 for b and -5 for c and simplify.

x=(4+/-sqrt(96))/8 which simplifies to

(1+sqrt6)/2 and (1-sqrt6)/2

Sorry, but my computer doesn't have the square root symbol

Answer 4

the quadratic formula is used to medical care the a wager variable ideas in quadratic equations, that are equations wherein the a variable is squared. the formula itself is: x = -b (+/-) (sq. root of (b^2-4ac) / 2a so given 2x^2 +9x + 4 a= 2 b= 9 c= 4 so then plugging it into the equation: x= (-9) (+/-) sq. root (9^2-4(2) (4) / 2(2) simplified: x= -9 (+/-) sq. root (40 9) / 4 x= (-9 + 7)/ 4 or (-9 - 7) /4 solved: x = -a million/2, or -4 choose that facilitates! stable achievement...

Answer 5

x=5/4x^2-4

Answer 6

4x^2-4x-5=0
=> (2x)^2 - 2(2x) - 5 = 0
Let 2x=y
y^2-2y-5=0
=> (y-sqrt(5)) = 0
=> y = sqrt(5)
=> 2x = sqrt(5)
hence x = sqrt(5) / 2

Answer 7

x=
(-1+ sqrt 6)/2
(-1 - sqrt 6)/2

Answer 8

4x^2-4x-5=0
x=(4+/-sqrt(16+4+4+5))/8=.5+/-sqrt(96)/8
x=.5+/-.5sqrt(6)
x=.5(1+/-sqrt(r)=1.725, -.725