Question

Please help this is my last problem and steps would be great working on notes for final on Friday!


Solve the equation in the real number system. what are the real solutions.
5x^3+8x^2-9x+2=0

Answer 1

Three solutions were found :

x = 2/5
x =(-2-√8)/2=-1-√ 2 = -2.414
x =(-2+√8)/2=-1+√ 2 = 0.414

Solve Quadratic Equation using the Quadratic Formula

2.4 Solving x2+2x-1 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC
x = ————————
2A

In our case, A = 1
B = 2
C = -1

Accordingly, B2 - 4AC =
4 - (-4) =
8

Applying the quadratic formula :

-2 ± √ 8
x = —————
2

Can √ 8 be simplified ?

Yes! The prime factorization of 8 is
2•2•2
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 8 = √ 2•2•2 =
± 2 • √ 2

√ 2 , rounded to 4 decimal digits, is 1.4142
So now we are looking at:
x = ( -2 ± 2 • 1.414 ) / 2

Two real solutions:

x =(-2+√8)/2=-1+√ 2 = 0.414

or:

x =(-2-√8)/2=-1-√ 2 = -2.414


Solving a Single Variable Equation :

2.5 Solve : 5x-2 = 0

Add 2 to both sides of the equation :
5x = 2
Divide both sides of the equation by 5:
x = 2/5

Answer 2

you are freaking awesome!!! Thank you so much!!!!