Question

Which are the solutions of the quadratic equation? x2 = 7x + 4

Answer 1

Answer: third option.

Step-by-step explanation:

Move the $7x$ and $4$ to the left side of the equation:

$x^2 = 7x+ 4$

 $x^2 -7x- 4=0$

Now you need to apply  the Quadratic formula:

$x=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

In this case you can identify that:

$a=1\\b=-7\\c=-4$

Then you can substitute values into the Quadratic formula and get the following solutions:

$x=\frac{-(-7)\±\sqrt{(-7)^2-4(1)(-4)} }{2*1}\\\\x_1=\frac{7-\sqrt{65} }{2}\\\\x_2=\frac{7+\sqrt{65} }{2}$

Answer 2

Step-by-step explanation:

$x {}^{2} = 7x + 4$

It can also be written as:-

$x {}^{2} - 7x - 4 = 0$

Now, here a=1, b= -7 and c = -4

Now by quadratic formula,

$d = b {}^{2} - 4ac$

Calculate d which is

$\sqrt{65}$

Now, the roots will be:-

$x = ( - b + \sqrt{d} ) \div 2a$

and hence it will become:-

$x = (7 + \sqrt{65} ) \div 2$

and

$x = (7 - \sqrt{65} ) \div 2$