Solve the equation x^2+3x-54=?

Question

Hence, solve (y+8/y)^2 +3(y+8/y)-54=0

Answer 1

x^2+3x-54 =0
D = 3² - 4 *1*(-54) = 225
x = (-3 + 15)/2 or x = (-3 - 15)/2
x = 6 or x = -9

(y+8/y)^2 +3(y+8/y)-54=0
y + 8/y = 6 or y + 8/y = -9
y² - 6y + 8 = 0 or y² +9y +8 = 0
D = 36 - 4*8 or D = 81 - 4*8
D = 4 or D = 49
y = (6 + 2)/2 or y = (6 - 2)/2 or y = (-9 + 7)/2 or y = (-9 - 7)/2
y = 4 or y = 2 or y = -1 or y = -8

Answer 2

the equation
x^2+3x-54 =0
the discriminant is b^2-4ac giving the equation
3² - 4 *1*(-54) = 225

applying the quadratic formula...
x = (-3 + 15)/2 or x = (-3 - 15)/2
x = 6 or x = -9

Next equation...
(y+8/y)^2 +3(y+8/y)-54=0
Substituting the data from the first equation...
y + 8/y = 6 or y + 8/y = -9
giving now the equations...
y² - 6y + 8 = 0 or y² +9y +8 = 0

getting the discriminant will give
D = 36 - 4*8 or D = 81 - 4*8
D = 4 or D = 49
then...
y = (6 + 2)/2 or y = (6 - 2)/2 or y = (-9 + 7)/2 or y = (-9 - 7)/2

Therefore...
y = 4 or y = 2 or y = -1 or y = -8

Answer 3

Firstly, try to find two numbers which when multiplied together give you -54 and when added together, give you 3. 9 x -6 = -54. 9 + -6 = 3
We can now write the equation as x^2+9x-6x-54=0
Factorising gives
x(x+9)-6(x+9)=0
therefore
(x-6)(x+9)^2=0
To get zero when multiplying two numbers together, one of the numbers HAS to be zero. This means that either x-6 or (x=9)^2 is zero.

If (x+9)^2 is zero, x+9 must be equal to xero. This implies that x can take the value of -9.

If x-6 is zero, x can take on the value of 6.

Solution, x=6 or x=-9.

I can see that you have substituted x=y+8/y

By substituting firstly that x=6, you will end up with the equation y^2-6y+8=0

By substituting x=-9, you will get the equation y^2+9y+8=0

Solve these two for yourself, using the above given steps. (hint: -2 X -4 = 8, -2 + -4 = -6, also, 8 X 1 =8, 8+1=9)

Goodluck!

Answer 4

Ok, you want to solve
x^2 + 3x - 54 = 0. Try factoring

(x +9 )(x -6 ) = 0, so
x +9 = 0 | x-6 = 0
x = -9 | x = 6.

NOW, x = y + 8/y, so solve

y + 8/y = -9 and y+8/y = 6.

I will do y + 8/y = -9. multiply both sides by y or

y^2 + 8 = -9y, bring together

y^2 + 9y + 8 = 0. This is factorable, so
(y+8)(y+1)=0, or

y = -8| y = -1.

Do the other one, and you are done.

Answer 5

When you factorise x^2+3x-54=0
You get; (x-9)(x+6)=0
Therefore x=9 or x=-6.

When you compare the two equations from the question, you notice that the only difference is that x is replaced by "(y+8/y)".

Therefore we can conclude that x=(y+8/y)
Therefore (y+8/y)=9 or (y+8/y)=-6

Those two equations can easily be solved to give you the two possible values of y.

Answer 6

(x+9)(x-6), so x = -9, x = 6. Then
y+8/y = -9, or y^2 +9y + 8 = 0 ==> y = -1, - 8
y+8/y = 6, or y^2 -6y + 8 = 0 ==> y = 2, 4

Answer 7

A. x^2+3x-54=0, get the factors of the eq:
(x+9)(x-6)=0, set each factor to zero
x+9=0; x-6=0, then, transpose to get the value of x
x=-9; x=6
B. y^2+64/y^2+3y+24/y-54=0; LCD is y^3 and you will get
(y^5+64y+3y^4+24y^2-54y^3)/y^3=0; multiply both sides with y^3 and you will get:
y^5+64y+3y^4+24y^2-54y^3=0; get the common factor and work it out from there...

Answer 8

x^2+3x-54=
(x+9)(x-6)= solutions x= -9 and x=6


y^2 + 2 + (64/y^2) + ( 3y+24/y) -54 = 0
y^2 - 52 + ( 64/y^2 ) + ( 3y + 24/y) = 0
y^2 + 3y +2 + ( 64/y^2 ) + (24/y) - 54 = 0
(y+1)(y+2)+ 2[ (32/y^2) + 3 (4 / y) - 9 ] = 0

Answer 9

x² + 3x - 54 = 0
(x + 9) (x - 6) = 0
x = - 9 , x = 6

y + 8/y = - 9
y² + 8 = - 9y
y² + 9y + 8 = 0
(y + 1) (y + 8) = 0
y = - 1 , y = - 8

y + 8/y = 6
y² + 8 = 6y
y² - 6y + 8 = 0
(y - 4) (y - 2) = 0
y = 2 , y = 4

Answer 10

x^2 + 3x - 54 = 0
(x + 9) (x - 6)

x + 9 = 0
x = - 9

x - 6 = 0
x = 6