Question

What are the solutions of the quadratic equation x2=9x+6

Answer 1

Question: What is the solution to the equation
`\bold{x\cdot \:2=9x+6}`

Answer:
`\boxed{\bold{x=-(6)/(7)}}`

Explanation:
`\downarrow{\downarrow{\downarrow{}}}`

[ Step One] Subtract 9x From Both Sides Of Equation

`\bold{x\cdot \:2-9x=9x+6-9x}`

[ Step Two ] Simplify Equation

`\bold{-7x=6}`

[ Step Three ] Divide Both Sides By -7

`\bold{(-7x)/(-7)=(6)/(-7)}`

[ Step Four ] Simplify

`\bold{x=-(6)/(7)}`

`\bold{\rightarrow{}Rhythm \ Bot\leftarrow{}}`

Answer 2

Answer: The required solutions of the given quadratic equation are

`x=(9+√(105))/(2),~~~(9-√(105))/(2).`

Step-by-step explanation: We are given to find the solution of the following quadratic equation :

`x^2=9x+6~~~~~~~\Rightarrow x^2-9x-6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

the solution of a quadratic equation of the form
`ax^2+bx+c=0,~a\\eq 0` is given by

`x=(-b\pm√(b^2-4ac))/(2a).`

For the given equation (i), we have

a = 1, b = -9 and c = -6.

Therefore, the solution of equation (i) is as follows :

`x\\\\\\=(-b\pm√(b^2-4ac))/(2a)\\\\\\=(-(-9)\pm√((-9)^2-4*1*(-6)))/(2*1)\\\\\\=(9\pm√(81+24))/(2)\\\\\\=(9\pm√(105))/(2).`

Thus, the required solutions of the given quadratic equation are

`x=(9+√(105))/(2),~~~(9-√(105))/(2).`