Question

Solve for x in the equation x^2-12x+36=90

Answer 1

If i'm correct your answer should be x =
`3 √(10) + 6`. Hope it helps!

Answer 2

`x=6-3√(10)\text{ or }x=6+3√(10)`

Explanation:

We have been given an equation
`x^2-12x+36=90`. We are asked to solve for x in our given equation.

We can see that left side of our given equation is a perfect square.

`(x-6)^2=90`

We will take square root of both sides of our given equation to solve for x.

`√((x-6)^2)=\pm√(90)`

Using radical rule
`\sqrt[n]{a^n}=a`, we will get:

`x-6=\pm√(90)`

`x-6=\pm√(9\cdot 10)`

`x-6=\pm√(3^2\cdot 10)`

`x-6=\pm√(3^2)\cdot √(10)`

Using radical rule
`\sqrt[n]{a^n}=a`, we will get:

`x-6=\pm3√(10)`

Now, we will add 6 on both sides of our given equation as:

`x-6+6=\pm 3√(10)+6`

`x=\pm 3√(10)+6`

`x=-3√(10)+6\text{ or }x=3√(10)+6`

`x=6-3√(10)\text{ or }x=6+3√(10)`

Therefore, the solution for our given equation would be
`x=6-3√(10)\text{ or }x=6+3√(10)`.