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

Question

asked Dec 21, 2019 18.3k views

2 Answers

Denian · Answer 1 · 2019-12-26T02:15:37+0000

Answer:

$x=6-3√(10)\text{ or }x=6+3√(10)$

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
$x=6-3√(10)\text{ or }x=6+3√(10)$ .