Answer: [tex]6+\sqrt{21}\ \text{and}\ 6-\sqrt{21}[/tex]
Step-by-step explanation:
Given
Quadratic equation is
[tex]x^2-12x+15=0[/tex]
Solving by completing the square method
[tex]\Rightarrow x^2-2\cdot 6\cdot x+15=0\\\text{add and subtract 36}\\\Rightarrow x^2-2\cdot 6\cdot x+15+36-36=0\\\Rightarrow x^2-2\cdot 6\cdot x+36+(-36+15)=0\\\text{using}\ (a-b)^2=a^2+b^2-2ab\\\Rightarrow (x-6)^2-21=0\\\Rightarrow (x-6)^2=21\\\Rightarrow x-6=\pm \sqrt{21}\\\Rightarrow x=6\pm \sqrt{21}[/tex]
The solution set of the equation is [tex]6+\sqrt{21}\ \text{and}\ 6-\sqrt{21}[/tex]
