Question

What are the solutionso of 8x^2 = 6 + 22x

Answer 1

8x² = 6 + 22x

Rearranging the quadratic equation, (Ax² + Bx + C = 0)
8x² - 22x - 6 = 0

Simplify. Divide both sides of the equation by 2.
4x² - 11x - 3 = 0

Using the quadratic formula. Identify first the value of the coefficients.
A = 4
B = -11
C = -3

Using the quadratic formula:


`x = (-B +- √(B^2 - 4AC) )/(2A)`

Substitute A, B and C


`x_(1) = (-(-11) + √((-11)^2 - 4(4)(-3)) )/(2(4))`

x = 3


`x_(1) = (-(-11) - √((-11)^2 - 4(4)(-3)) )/(2(4))`

x =
`- (1)/(4)`

Answer 2

You can get all the terms on one side, and then solve for x by any means:

`0 = -8x^2+22x+6`

Factor out a -2:

`0 = -2(4x^2-11x-3)`

Factor this equation:

`0 = 4x^2-11x-3`

I will use the AC method. To use it, first multiply a and c (in ax^2 + bx +c):

`4*-3 = -12`

Now, look for two numbers that multiply to -12 and add to -11. Obviously these numbers are -12 and 1. (-12*1 = -12 and -12+1 = -11). Now, because of rules, you set it up in a Punnett square:

4x^2 -12x
x -3

Now, we find common factors of the terms in rows:
_x_______-3__
4x| 4x^2 -12x
1 | x -3

So, you can use this to write an equivalent expression to the quadratic given:

`(x-3)(4x+1)`

Now, we known the factors are (solve for x): 3 and -1/4.