Question

3(x-4)squared - 5(x - 4) = 12​

Answer 1

Answer:

3(x-4)² - 5(x-4) = 12

First expand them,

3(x²+16-8x) -5(x-4) = 12

=> 3x² + 48 - 24x -5x + 20 = 12,

=> 3x² - 29x + 56 = 0,

Now use the quadratic equation formula, or find the factors,

In general x of quadratic equation is,

\frac{( -b + - \sqrt{ {b}^{2} - 4ac} )}{2a}

2a

(−b+−

b

2

−4ac

)

Here a = 3, b = -29 , c = 56,

Inserting them in the formula we get,

(29+- √169 )/6 ,. b²-4ac = 169,

=> (29+-13)/6,

=> 42/6 and 16/6, are the roots,

=> 7 and 16/6,

=> 7, 8/3 are the roots

Keep them in the question, you will get 12,

There is another simpler method to do this problem,

3x² - 29x +56 = 0, can be written as,

3x² - 21x - 8x + 56 = 0,

Now taking common,

3x(x-7) -8(x-7) = 0,

Taking ( x-7 ) common,

(x-7)[3x-8] = 0

=> Either x -7 = 0 or 3x - 8 =0,

=> either x = 7 or x = 8/3, But as it is a quadratic , both are the roots of the equation,

Hope you understand,

Have a great day !!