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vladimir1956 [14]
3 years ago
12

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

Mathematics
2 answers:
djyliett [7]3 years ago
7 0
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 =  \frac{-B +-  \sqrt{B^2 - 4AC} }{2A}

Substitute A, B and C

x_{1} = \frac{-(-11)  + \sqrt{(-11)^2 - 4(4)(-3)} }{2(4)}
     
                 x = 3

x_{1} = \frac{-(-11) - \sqrt{(-11)^2 - 4(4)(-3)} }{2(4)}

                 x = - \frac{1}{4}



                    


liraira [26]3 years ago
3 0
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.
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