How do you solve #\sqrt{x}=x-6#?
3 Answers
Explanation:
Square the equation:
Apply the expansion of
Factorize the quadratic.
Note that substituting 4 in the equation returns 2 = -2, which is obviously wrong. So we neglect x = 4 in the set of solutions. Take care to verify your answers after solving(don't make my mistake!)
Explanation:
First, square both sides:
Simplify:
Move everything to one side of the equation:
Now we need to factor.
Our equation is standard form, or
The factored form is
We have two rules to find
#m# and#n# have to multiply up to#a * c# , or#36# #m# and#n# have to add up to#b# , or#-13#
Those two numbers are
Therefore,
However, we still need to check our answers by substituting them back into the original equation, since we have a square root in our original equation.
Let's first check if
This is not true! That means that
Now let's check
This is true! That means that
So the final answer is
Hope this helps!
Explanation:
First, square both sides of this equation.
Now put in standard form.
Factor.
When we squared both sides to at the beginning, we enabled an extraneous solution since