Given equation to us is [tex] x^2+4=8x+5[/tex]
And we need to find out the solutions to the given equation. We can rewrite the equation as ,
[tex]\longrightarrow x^2+4-8x-5=0 [/tex]
Simplify,
[tex]\longrightarrow x^2-8x-1=0[/tex]
Now this equation is in standard form of quadratic equation which is [tex]ax^2+bx+c=0[/tex]
With respect to the standard form ,
Now we may use the quadratic formula for finding the roots as ,
[tex]\longrightarrow x =\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\ [/tex]
So that,
[tex]\longrightarrow x =\dfrac{-(-8)\pm\sqrt{-8^2-4(1)(-1)}}{2(1)}\\[/tex]
[tex]\longrightarrow x =\dfrac{8\pm\sqrt{64+4}}{2}\\[/tex]
[tex]\longrightarrow x =\dfrac{8\pm \sqrt{68}}{2}\\ [/tex]
[tex]\longrightarrow x =\dfrac{8\pm 2\sqrt{17}}{2}\\ [/tex]
[tex]\longrightarrow\underline{\underline{ x = 4\pm \sqrt{17}}} [/tex]
And we are done!
