Question 1

Solve: x−6−−−−−√=x−6 . Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter.

Question 2

ANSWER:

x = 6; 7

Explanation:

We have the following equation:

We solve for x:

$\begin{gathered} \left(√(x-6)\right)^2=\left(x-6\right)^2 \\ \\ x-6=x^2-12x+36 \\ \\ x^2-12x-x+36+6=0 \\ \\ x^2-13x+42=0 \\ \\ -13x=-6x-7x \\ \\ x^2-6x-7x+42=0 \\ \\ \left(x^2-6x\right)+\left(-7x+42\right)=0 \\ \\ x\left(x-6\right)-7\left(x-6\right) \\ \\ \left(x-6\right)\left(x-7\right)=0 \\ \\ x-6=0\rightarrow x=6 \\ \\ x-7=0\operatorname{\rightarrow}x=7 \\ \\ \text{ We check each solution, as follows:} \\ \\ √(6-6)=6-6\rightarrow0=0\rightarrow\text{ True} \\ \\ √(7-6)=7-6\rightarrow1=1\rightarrow\text{ True} \\ \\ \text{ Both solutions are correct therefore:} \\ \\ x=6;7 \end{gathered}$

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