The roots of the given quadratic equation by completing the square method is [tex]3+2\sqrt{6}[/tex] and [tex]3-2\sqrt{6}[/tex].
What is completing the square method?
Completing the square method is one of the methods to find the roots of the given quadratic equation. In this method, we have to convert the given equation into a perfect square.
According to the given question.
We have a quadratic equation
[tex]x^{2} -6x = 15..(i)[/tex]
By completing the square method the roots of the above equation is given by
[tex]x^{2} -6x-15=0[/tex]
⇒[tex]x^{2} -2(3)x+(3)^{2} -(3)^{2} -15=0[/tex]
⇒ [tex](x-3)^{2} -9-15=0[/tex]
⇒[tex](x-3)^{2} =24\\[/tex]
⇒[tex]x -3 =[/tex]±[tex]\sqrt{24}[/tex]
⇒[tex]x-3=[/tex]±[tex]2\sqrt{6}[/tex]
⇒[tex]x = 3[/tex]±[tex]2\sqrt{6}[/tex]
⇒[tex]x = 3+2\sqrt{6}[/tex] 0r [tex]3-2\sqrt{6}[/tex]
Hence, the roots of the given quadratic equation by completing the square method is [tex]3+2\sqrt{6}[/tex] and [tex]3-2\sqrt{6}[/tex].
Find out more information about completing the square method here:
https://brainly.com/question/26107616
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