Question: "Find the solution: 6=x2−2x+12"

High School
Algebra
Algebra I
Exponents and radicals

abondantQ

Answered question

2021-09-22

Find the solution:

6 = \sqrt{x^{2} - 2 x + 12}

Answer & Explanation

Jayden-James Duffy

Skilled2021-09-23Added 91 answers

Radical or Exponents or Power is defined as the number of times that a variable or constant is being repeated. It is also called power raised. Exponents are used to describing number of times in a single notation
The radical equation given to us
$6 = \sqrt{x^{2} - 2 x + 12}$
To find the solution for the given radical equation
Solution to the question
We have,
$6 = \sqrt{x^{2} - 2 x + 12}$
Squaring both sides we obtain,
$6^{2} = {(\sqrt{x^{2} - 2 x + 12})}^{2}$
$36 = x^{2} - 2 x + 12$
$x^{2} - 2 x + 12 - 36 = 0$
$x^{2} - 2 x - 24 = 0$
$x^{2} - 6 x + 4 x = 0$
$x (x - 6) + 4 (x - 6) = 0$
$(x + 4) (x - 6) = 0$
either $x = - 4 or x = 6$
There are two valid solutions $x = - 4 and x = 6$

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